Jan 4

Winter Session Begins
Wednesday, January 4, 2017

Jan 24

Winter Session ends
Tuesday, January 24, 2017

Jan 30

Spring Classes Begin
Monday, January 30, 2017

Feb 7

Graduate Mentoring Seminar/Introductory Talks-Dr. Yiqiang Li
Dynkin diagram stampede
5:00PM, Tue Feb 7 2017, Math 250

I’ll present some examples in Lie theory and geometry unified under Dynkin diagrams.

Feb 9

Department Faculty Meeting
4:00PM, Thu Feb 9 2017, Math 250

Feb 10

G&T seminar
Tim Riley (Cornell)
What calculating in the trivial group has to do with RNA-folding, the design of liquid crystals, and counting fixed points
4:00PM, Fri Feb 10 2017, Math 122

I will give polynomial-time dynamic-programming algorithms finding the "areas" of words in certain presentations of the trivial group. I will explain how this relates to RNA-folding, the design of liquid crystals, and counting fixed points of self-maps of compact surfaces.

Feb 13

AWM/Algebra Seminar- Amber Russell, Butler University
“The Springer Correspondence and Related Topics”
4:00PM, Mon Feb 13 2017, Math 250

Title: “The Springer Correspondence and Related Topics”

Feb 14

Applied Math Seminar- Jun Zhuang, University at Buffalo
TBA
3:45PM, Tue Feb 14 2017, Math 250

TBA

Feb 14

Graduate Mentoring Seminar/Introductory Talks- Dr. Jingbo Xia
Operators on the Drury-Arveson space
5:00PM, Tue Feb 14 2017, Math 250

Title: Operators on the Drury-Arveson space

Feb 15

Analysis Seminar-Jingbo Xia, University at Buffalo
On the essential commutant of the Toeplitz algebra on the Bergman space
4:00PM, Wed Feb 15 2017, Math 250

Title: On the essential commutant of the Toeplitz algebra on the Bergman space

Feb 15

AWM Lecture Series
“Women Talk Math (And Other Things)"
4:00PM, Wed Feb 15 2017, 732 Clemens Hall

“Women Talk Math (And Other Things)"

Feb 20

Algebra Seminar- Qing Zhang, Ohio State
A local converse theorem for U(2,2)
4:00PM, Mon Feb 20 2017, Math 250

In the theory of representation of p-adic groups, the local converse problems ask if one can characterize a generic irreducible representation \pi of G(F) by the gamma factors of its various twists with GL_k(F), where G is a reductive group, F is a p-adic field, and k varies in a set depends on G. In this talk, we will sketch a proof of a local converse theorem for the unitary group U(2,2).

Feb 21

Applied Math Seminar-Kazuo Yamazaki, University of Rochester
TBA
3:45PM, Tue Feb 21 2017

TBA

Feb 21

Graduate Mentoring Seminar/Introductory Talks- Dr. Sarah Muldoon
Network Neuroscience
5:00PM, Tue Feb 21 2017, Math 250

Network Neuroscience is a rapidly growing field of research that draws upon tools from network theory to understand the brain as a complex system of interacting elements. In this talk, I'll describe research in my group to develop novel techniques and measures to investigate and quantify the role of network organization in brain function. This work is heavily data-driven and I will explain how we build brain networks using a multitude of different types of neuroscience data spanning a wide range of spatial and temporal scales. I'll then give a brief overview of the types of problems we are currently investigating, ranging from the development of improved algorithms for the detection of community structure in multilayer networks, to computational modeling of brain dynamics, to understanding the role of modified network structure in altered brain dynamics associated with epilepsy.

Feb 27

AWM Lecture Series- Diane Henderson
TBA
5:00PM, Mon Feb 27 2017, Math 250

TBA

Feb 28

Applied Math Seminar-Mathew J. Hoffman, RIT
TBA
3:45PM, Tue Feb 28 2017, Math 250

TBA

Feb 28

Graduate Mentoring Seminar/Introductory Talks- Dr. Brian Spencer
Free boundary problems in materials science
5:00PM, Tue Feb 28 2017, Math 250

I give an introduction to the applied mathematics of materials science, focusing on the area of pattern formation and free boundary problems as applied to microstructure formation and crystal growth of materials.

Mar 3

G&T seminar
Johanna Mangahas (Buffalo)
Normal right-angled Artin groups in mapping class groups
4:00PM, Fri Mar 3 2017, Math 122

Free normal subgroups of mapping class groups abound, by the result of Dahmani, Guirardel, and Osin that the normal closure of high powers of pseudo-Anosovs is free. At the other extreme, if a normal subgroup contains a mapping class supported on too small a subsurface, it can never be isomorphic to a right-angled Artin group, by work of Brendle and Margalit. I will talk about a case right in between: a family of normal subgroups isomorphic to non-free right-angled Artin groups. We also recover, expand, and make constructive the result of Dahmani, Guirardel, and Osin about free normal subgroups. We do this by creating a version of their "windmill" construction tailor-made for the projection complexes introduced by Bestvina, Bromberg, and Fujiwara. This is joint work with Matt Clay and Dan Margalit.

Mar 6

Algebra Seminar- Jack Buttcane, University at Buffalo
Higher weight on GL(3).
4:00PM, Mon Mar 6 2017, Math 250

Classical automorphic forms are generally attached to subgroups of Gamma = SL(2,Z) and are functions on Gamma\H = Gamma\PSL(2,R)/SO(2,R). The come in two flavors: holomorphic modular forms and (spherical or weight 0) Maass forms. These two types of automorphic forms are both special cases of Maass forms with weight, and they collectively generate a basis of L^2(Gamma\PSL(2,R)). The spherical Maass forms have been generalized to subgroups of SL(n,Z), and these are currently a popular topic of study, particularly on SL(3,Z). This talk will describe the generalization to Maass forms with weight on SL(3,Z), the new types of non-spherical forms that arise, and what is currently known about them.

Mar 7

Applied Math Seminar- Sean Nixon (SUNY Geneseo)
3:45PM, Tue Mar 7 2017, Math 250

Mar 7

Graduate Mentoring Seminar/Introductory Talks- Dr. Xingru Zhang
A quick trip through knot theory
5:00PM, Tue Mar 7 2017, Math 250

This is an informal introductory talk
on knot theory. A knot is the image of an embedded
circle in the 3-sphere. Two knots are equivalent
if one can be deformed into the other without
tearing or self-crossing.
A fundamental problem in knot theory is to distinguish
knots up to equivalence. I'll try to explain as non-techniquely as possible how people approach this problem
using various knot invariants and how knot theory
is connected to low dimensional topology.
The talk is aimed at students who have taken a course on
topology.

Mar 8

Analysis Seminar- Byung-Jay Kahng, Canisius College
Invariant weights on a locally compact quantum groupoid
4:00PM, Wed Mar 8 2017, Math 250

Motivated by the purely algebraic notion of ``weak multiplier Hopf algebras'', we develop the definition of a class of locally compact quantum groupoids in the C*-algebra framework. Existence of a certain canonical idempotent element plays an important role. As in the quantum group case, we require left and right Haar weights but the antipode is not explicitly defined. This class would contain all locally compact quantum groups, and form a self-dual category.
In this talk, we will focus on how to formulate the left and right invariance conditions, similar to but different from the quantum group case. We will gather some alternative forms of the invariant conditions. Then we will explore the central roles these invariant weights play in the quantum groupoid theory, in the construction of the regular representations (in terms of certain partial isometries) and the antipode map.
This is based on an on-going joint work with Alfons Van Daele (Leuven).

Mar 10

G&T seminar
Marco Varisco (SUNY-Albany)
On Whitehead groups of infinite groups with torsion
4:00PM, Fri Mar 10 2017, Math 122

Given a group G (finite or infinite, abelian or not), its Whitehead group Wh(G) is an abelian group defined using elementary linear algebra. Remarkably, as I will review, Whitehead groups play an important role in the classification of high-dimensional manifolds. Unfortunately, Whitehead groups are very hard to compute. I will overview what is known and what is conjectured about the structure of Whitehead groups. Then I will present joint work with Wolfgang Lück, Holger Reich, and John Rognes [Adv. Math. 304 (2017), 930–1020, arXiv:1504.03674] and with Ross Geoghegan [arXiv:1401.0357] about Whitehead groups of certain infinite groups with torsion, including outer automorphism groups of free groups, and Thompson’s group T.

Mar 13

Special Talk- Kevin Troyanos, SVP Marketing Analytics Saatchi & Saatchi Wellness
Exploring a Career in Marketing Analytics and Data Science
5:00PM, Mon Mar 13 2017, Math 250

Title: Exploring a Career in Marketing Analytics and Data Science
Learn how the advertising industry is leveraging math, data, computation, and algorithms to uncover and predict behaviorial insights that ultimately lead to smarter marketing decisions.

Mar 14

Applied Math Seminar-Michael Langberg, University at Buffalo
TBA
3:45PM, Tue Mar 14 2017, Math 250

TBA

Mar 14

Graduate Mentoring Seminar/Introductory Talks- Dr. Jae-Hun Jung
High order numerical approximations for interpolations and PDEs
5:00PM, Tue Mar 14 2017, Math 250

In this talk, I will briefly explain my research in numerical analysis and scientific computing. In the first part of my talk, I will introduce several research projects that I have finished with students and share my research experience with high school students to graduate students. In the second part of my talk, I will explain, by example, how to use the global polynomial interpolation in images and solutions to PDEs, particularly the high order adaptive method based on the orthogonal polynomials and non-polynomial bases such as radial basis functions and frames that we recently developed.

Mar 20

Spring Recess
Monday, March 20, 2017

Mar 27

Classes Resume
Monday, March 27, 2017

Mar 28

Applied Math Seminar-Ferdinand Schweser, University of Buffalo
TBA
3:45PM, Tue Mar 28 2017, Math 250

TBA

Apr 3

Algebra Seminar- Baiying Liu, Purdue University
On the local converse theorem for GLn
4:00PM, Mon Apr 3 2017, Math 250

In this talk, I will introduce a complete proof of a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field. This is a joint work with Prof. Herve Jacquet.
I will also talk about extensions of local converse theorem to the setting of l-adic families and modular l representations, which is a joint work with Gilbert Moss.

Apr 4

Applied Math Seminar-Matt Tranter, Loughborough University
TBA
3:45PM, Tue Apr 4 2017, Math 250

TBA

Apr 6

Applied Math Seminar *Note/ Special Day
James Boyle, University at Buffalo
3:45PM, Thu Apr 6 2017, Math 250

Apr 10

Algebra Seminar- Muthukrishnan Krishnamurthy, University of Iowa
On a converse theorem for GL(n)
4:00PM, Mon Apr 10 2017, Math 250

A typical converse theorem gives a characterization of automorphic representations of GL(n) in terms of the analytic properties of certain twisted L-functions. In this talk, I will explain a theorem that uses only twists by unramified automorphic representations of GL(n-1). This is a generalization of an earlier result by Cogdell and Piatetski-Shapiro.

Apr 14

G&T seminar
Tolga Etgü (Koç/Princeton)
Fukaya categories of plumbings and multiplicative preprojective algebras
4:00PM, Fri Apr 14 2017, Math 122

I will talk about the wrapped Fukaya category of the Weinstein manifold obtained by plumbing copies of cotangent bundles of surfaces. A symplectic handlebody decomposition of this manifold will be described. As objects of the Fukaya category, the cocores of the 2-handles provide a generating set whose endomorphism algebra turns out to be quasi-isomorphic to the derived multiplicative preprojective algebra associated to the plumbing graph. This talk is based on joint work with Yanki Lekili.

Apr 18

Applied Math Seminar-Yang Yang, Michigan Tech
TBA
3:45PM, Tue Apr 18 2017, Math 250

TBA

Apr 20

Tenured Faculty Meeting
4:00PM, Thu Apr 20 2017, Math 250

Apr 21

G&T seminar
Abigail Thompson (UC Davis)
An invariant of trisected 4-manifolds
4:00PM, Fri Apr 21 2017, Math 122

A closed, orientable 3-manifold M always has a Heegaard splitting, that is, M^3 can be described as the union of two handlebodies glued together along their boundaries. Gay and Kirby extended this idea to 4-manifolds, showing that any closed orientable 4-manifold M^4 can be described as the union of three 4-dimensional handlebodies, glued together (carefully) along their boundaries. They called this a trisection of M^4. I’ll discuss their result, and describe a natural 4-manifold invariant, L(M^4), that arises from this decomposition. This is joint work with D. Gay and R. Kirby.

Apr 25

Applied Math Seminar- Antonio Moro, Northumbria University
TBA
3:45PM, Tue Apr 25 2017, Math 250

TBA

Apr 27

Applied Math Seminar-Michael Langberg, University at Buffalo, Electrical Engineering
3:45PM, Thu Apr 27 2017,

Apr 28

G&T seminar
Jonah Gaster (Boston College)
Combinatorial properties of curve graphs
4:00PM, Fri Apr 28 2017, Math 122

The curve graph of a closed oriented surface of genus g has vertices given by simple closed curves, and edges that correspond to curves that can be realized disjointly. Inquiry into the large scale geometry of these graphs has borne considerable fruit, and lead to the resolution of some of Thurston's conjectures. We will take a more naive perspective and explore instead combinatorial properties of this graph. For instance, what is its chromatic number (finite due to work of Bestvina-Bromberg-Fujiwara)? What are its induced subgraphs? Though precise answers to these questions are currently beyond reach, we will present progress that informs them.

May 2

Applied Math Seminar-Ming Yan, Michigan State
TBA
3:45PM, Tue May 2 2017, Math 250

TBA

May 3

Analysis Seminar
Brandon Seward, Courant Institute
Positive entropy actions of countable groups factor onto Bernoulli shifts
4:00PM, Wed May 3 2017, Math 250

I will show that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well known Sinai factor theorem from classical entropy theory. A consequence of this theorem is that every positive-entropy free ergodic action of a non-amenable group satisfies the measurable von Neumann conjecture.

May 5

G&T seminar
Sam Taylor (Yale)
Veering triangulations and fibered faces of 3--manifolds
4:00PM, Fri May 5 2017, Math 122

From a pseudo-Anosov homeomorphism of a surface, Agol’s veering triangulation gives a canonical ideal triangulation of the associated mapping torus punctured along singular fibers. By recent work of Gueritaud, this triangulation can be directly obtained from the stable and unstable laminations of the monodromy. We study the way in which these triangulations interact with the arc complexes of fibers and their subsurfaces. In particular, we find that the veering triangulation records the hierarchy of subsurface projections associated to each fiber in a fibered face of the Thurston norm ball. These projections are in fact visible as embedded subcomplexes of the veering triangulation itself. Through this structure, we obtained explicit control over the size and nature of subsurface projections occurring over a fixed fibered face. This is joint work with Yair Minsky.

May 8

Algebra Seminar- Matt Douglass (NSF & University of North Texas)
Schur-Weyl duality and the free Lie algebra
4:00PM, Mon May 8 2017, Math 250

Schur-Weyl duality, which goes back to Schur's thesis in 1927, may be phrased as the pair of assertions that (1) any endomorphism of the vector space r-fold tensors of an n-dimensional vector space V that commutes with all permutations of the factors arises from the diagonal action of the algebra of linear transformations of V and dually (2) any endomorphism of the vector space r-fold tensors of V that commutes with the diagonal action of the algebra of linear transformations of V arises from the permutation action of the rth symmetric group on the factors. In this talk I'll discuss the natural analog of Schur-Weyl duality when the space of r-fold tensors is replaced by the subspace of homogeneous, degree r, Lie polynomials. In this setting the rth symmetric group is replaced by a "Hecke" algebra that arises in a surprisingly different context. Studying the structure of this new algebra leads to intriguing combinatorial questions (and a sequence that does not appear in the Online Encyclopedia of Integer Sequences!).

May 9

Applied Math Seminar- Kanika Bansal, University at Buffalo
3:45PM, Tue May 9 2017, Buffalo

May 12

Last Day of Classes
Friday, May 12, 2017

May 12

G&T seminar
Steven Sivek (MPIM)
SU(2)-cyclic surgeries and the pillowcase
4:00PM, Fri May 12 2017, Math 122

The cyclic surgery theorem of Culler, Gordon, Luecke, and Shalen implies that any knot in S^3 other than a torus knot has at most two nontrivial cyclic surgeries. In this talk, we investigate the weaker notion of SU(2)-cyclic surgeries on a knot, meaning surgeries whose fundamental groups only admit SU(2) representations with cyclic image. By studying the image of the SU(2) character variety of a knot in the “pillowcase”, we will show that if it has infinitely many SU(2)-cyclic surgeries, then the corresponding slopes (viewed as a subset of RP^1) have a unique limit point, which is a finite, rational number, and that this limit is a boundary slope for the knot. As a corollary, it follows that for any nontrivial knot, the set of SU(2)-cyclic surgery slopes is bounded. This is joint work with Raphael Zentner.

May 13

Reading Days
Saturday, May 13, 2017

May 14

Reading Days
Sunday, May 14, 2017

May 15

Semester Finals Begin
Monday, May 15, 2017

May 19

Commencement Weekend
Friday, May 19, 2017

Aug 18

Summer Session "M" ends
Friday, August 18, 2017

Aug 28

Fall Classes Begin
Monday, August 28, 2017

Aug 31

Faculty Meeting
4:00PM, Thu Aug 31 2017, Math 250

Sep 4

Labor Day Observed (no classes)
Monday, September 4, 2017

Sep 5

Applied Math Seminar- Jose Carrillo, Imperial College
London
Swarming, Interaction Energies and PDEs
3:30PM, Tue Sep 5 2017, Math 250

I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random particle simulations, flocks and mills, and their qualitative behavior. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. Compactly supported global minimizers determine the flock patterns whose existence is related to the classical H-stability in statistical mechanics and the classical obstacle problem for differential operators.

Sep 5

Graduate Mentoring Seminar- Dr. William Menasco
"Menasco's Rules for Doing Research."
5:00PM, Tue Sep 5 2017, Math 250

"Menasco's Rules for Doing Research."

Sep 8

G&T Seminar
Piotr Hajac (Polish Academy of Sciences)
There and back again: from the Borsuk-Ulam theorem to quantum spaces
4:00PM, Fri Sep 8 2017, Math 122

Assuming that both temperature and pressure are continuous functions, we can conclude that there are always two antipodal points on Earth with exactly the same pressure and temperature. This is the two-dimensional version of the celebrated Borsuk-Ulam Theorem which states that for any continuous map from the n-dimensional sphere to n-dimensional real Euclidean space there is always a pair of antipodal points on the sphere that are identified by the map. Our quest to unravel topological mysteries in the Middle Earth of quantum spaces will begin with gentle preparations in the Shire of elementary topology. Then, after riding swiftly through the Rohan of C*-algebras and Gelfand-Naimark Theorems, and carefully avoiding the Mordor of incomprehensible technicalities, we shall arrive in the Gondor of compact quantum groups acting freely on unital C*-algebras. It is therein that the generalized Borsuk-Ulam-type statements dwell waiting to be proven or disproven. To end with, we will pay tribute to the ancient quantum group SUq(2), and show how the proven non-trivializability of Pflaum's SUq(2)-principal instanton bundle is a special case of two different noncommutative Borsuk-Ulam-type conjectures. Time permitting, we shall also explain a general method to extend the non-trivializability result from the Pflaum quantum instanton bundle to an arbitrary finitely iterated equivariant join of SUq(2) with itself. The latter is a quantum sphere with a free SUq(2)-action whose space of orbits defines a quantum quaternionic projective space. (Based on joint work with Paul F. Baum, Ludwik Dabrowski, Tomasz Maszczyk and Sergey Neshveyev.)

Sep 12

Applied Math Seminar- Vitali Vougalter, University of Toronto
3:45PM, Tue Sep 12 2017, Math 250

Sep 12

Graduate Mentoring Seminar-Dr. Bernard Badzioch
"Using LaTeX"
5:00PM, Tue Sep 12 2017, Math 250

"Using LaTeX"

Sep 14

Math Colloquium- Gufang Zhao, University of Massachusetts, Amherst.
From configuration of points on the punctured plane to Higgs bundles on an elliptic curve.
4:00PM, Thu Sep 14 2017, Math 250

There are many common numerical and combinatorial features in Schubet calculus, knots theory, and number theory. These features are algebraically controlled by Hecke-type algebras and their representations. In the first part of this talk, I will briefly review these correspondences. In particular, the affine Hecke algebra is related to configurations of points on the punctured plane; the double affine Hecke algebra is related to configurations of points on an elliptic curve. In the second part of this talk, I will introduce a link between these two algebras, called the elliptic affine Hecke algebra. It has a construction using elliptic Schubert calculus, and its irreducible representations are parameterized by nilpotent Higgs bundles on an elliptic curve.

Sep 15

Topology Day
Schedule:
Friday, September 15, 2017, Math 250

Schedule:
11:00-11:50 M. Khovanov (Columbia U.), How to categorify the ring of integers with two inverted.

12:10-1:00 A. Mathew (U. of Chicago), TBA

2:30-3:20 R. Lipshitz (U. of Oregon), Bordered Heegaard Floer homology and incompressible surfaces

3:50-4:40 C. Leininger (UIUC), Surface bundles over Teichmuller curves.

Sep 18

Math Colloquium- Daqing Wan (University of California at Irvine)
Stability of Zeta Functions over Finite Fields
3:00PM, Mon Sep 18 2017, Math 250

For a curve C over a finite field F_q of characteristic p,
the zeta function of C counts the number of rational points of C
over every finite extension of F_q. The zeta function is a rational
function satisfying a Riemann hypothesis by Weil's celebrated theorem.
In this introductory talk, we discuss the p-adic counterpart of the
Riemann hypothesis, focusing on its stability when the curve moves
in a family or in a tower.

Sep 18

Myhill Lecture Series- Guoliang Yu, Texas A & M University
Rigidity problems in geometry and topology
4:00PM, Mon Sep 18 2017, Math 250

In this lecture, I will introduce certain rigidity problems in geometry and topology of manifolds and give a survey on their recent progress.

Sep 19

Myhill Lecture Series- Guoliang Yu, Texas A & M University
Geometry and complexity of groups
4:00PM, Tue Sep 19 2017, Math 250

In this lecture, I will describe various notions of complexity in geometric group theory and explain how these concepts are related to rigidity of manifolds.

Sep 20

Myhill Lecture Series- Guoliang Yu, Texas A & M University
Higher invariants of elliptic operators
4:00PM, Wed Sep 20 2017, Math 250

In this lecture, I will introduce primary and secondary invariants of elliptic operators and apply these invariants in the study of rigidity and nonrigidity problems in geometry and topology.

Sep 22

G&T Seminar
Devin Murray (Brandeis)
Groups, rigidity, and the Morse boundary
4:00PM, Fri Sep 22 2017, Math 122

In geometric group theory a finitely presented group is often
identified with its Cayley graph. Unfortunately, the Cayley graph
depends on the generating set of the group. When the generating set is
changed the homeomorphism type of the graph can change quite a lot.
However, there is a metric equivalence relation called a quasi-isometry
(QI) and the Cayley graph *is* well defined up to quasi-isometries.
Unfortunately quasi-isometries are a very weak geometric equivalence
(in general there may be no continuous bijections between quasi-
isometric spaces!). In this context a very natural question to ask is,
if two groups are quasi-isometric how similar are they as groups? For
some classes of groups the answer is quite surprising! For example, if
a group G is QI to \pi_1(S) where S is a surface group, then G is
(virtually) isomorphic to a surface group! A class of groups which
exhibits this property is called quasi-isometrically rigid.

Many classes of groups are quasi-isometrically rigid, free abelian
groups, finite volume discrete subgroups of a non-compact Lie group,
surface groups, etc. Often, some form of negative curvature plays an
important role in proving rigidity style theorems.

The Morse property is a natural generalization of the behavior of
geodesics in negatively curved manifolds. The Morse boundary is a
quasi-isometry invariant for finitely generated groups that serves a
similar role that the boundary of hyperbolic n-space serves for
hyperbolic manifold groups. I will introduce all of the objects in
question and talk about some results for the morse boundary that make
it a promising tool to study the quasi-isometric rigidity phenomena of
some classes of groups, in particular some CAT(0) groups, Mapping Class
groups, some artin/coxeter groups etc.

This is joint work with Ruth Charney and Matt Cordes.

Sep 26

Applied Math Seminar- Gourab Ghoshal, University of Rochester
3:45PM, Tue Sep 26 2017, Math 250

Sep 26

Graduate Mentoring Seminar- Dr. David Hemmer
An Introduction to Mathematical Publishing for graduate students.
5:00PM, Tue Sep 26 2017, Math 250

An Introduction to Mathematical Publishing for graduate students.

Sep 27

Analysis Seminar-Mehrdad Kalantar, University of Houston
Boundary actions and applications to rigidity problems in operator algebras.
4:00PM, Wed Sep 27 2017, Math 250

We show how boundary actions in the sense of Furstenberg can be applied to some rigidity problems in operator algebras. In contrast to previous work, we apply measurable boundaries in C*-algebra context, and topological boundaries in von Neumann algebraic setting.
This is joint work with Yair Hartman.

Oct 2

Algebra Seminar- Alexander Shapiro, University of Toronto
Positive representations of quantum groups.
4:00PM, Mon Oct 2 2017, Math 250

Positive representations are certain bimodules for a
quantum group and its modular dual. In 2001, Ponsot and Teschner
constructed these representations for $U_q(\mathfrak{sl}_2)$ and
proved that they form a continuous braided monoidal category, where
the word "continuous" means that a tensor product of two
representations decomposes into a direct integral rather than a direct
sum. Ten years later, their construction was generalized to all other
types by Frenkel and Ip. Although the corresponding categories were
braided more or less by construction, it remained a conjecture that
they are monoidal. Following a joint work in progress with Gus
Schrader, I will discuss the proof of this conjecture for
$U_q(\mathfrak{sl}_n)$. The proof is based on our previous work where
the quantum group is realized as a quantum cluster $\mathcal
X$-variety. If time permits, I will outline a relation between this
story and the modular functor conjecture in higher Teichmüller theory
along with several other applications.

Oct 3

Applied Math Seminar- Jie Sun,Clarkson University
Computational Network Inference from Data
3:45PM, Tue Oct 3 2017, Math 250

Understanding the dynamics and functioning of complex systems is one of the most challenging tasks faced in modern science. A central problem to tackle is to accurately and reliable infer the underlying cause-and-effect (i.e., causal) network from observational data, especially when the system consists of a large number of interacting components and the dynamics can be intrinsically nonlinear. In this talk I will review my recent collaborative projects on optimal causation entropy (oCSE) as a general framework to reconstruct networks (whose edges are hidden) from data measured on the nodes. Depending on the context, the framework can be adapted to incorporate prior information of noise distributions, and also to accommodate both longitudinal and non-longitudinal data. I will show results of applying oCSE to synthetic datasets (as benchmark) as well as real-world datasets in several different disciplines. Examples of application include discovering ``social” interaction in swarming insects, detecting structural patterns and damages in bridges, as well as fitting Boolean functions to genotype-phenotype data. Time permits I will also discuss a few other related problems, including data fusion network reconstruction, uncertainty quantification, and visualization of bipartite network data.

Oct 3

Graduate Mentoring Seminar- Dr. William Menasco
"Documenting Your Achievements."
5:00PM, Tue Oct 3 2017, Math 250

"Documenting Your Achievements."

Oct 4

Analysis Seminar
Yi Wang, Texas A&M University
Title of the Talk: On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains
4:00PM, Wed Oct 4 2017, Room 250, The Math Building

We show that under a mild condition, a principal submodule of the Bergman module on a strongly pseudoconvex domain, generated by a holomorphic function defined on a neighborhood of its closure, is p essentially normal for p>n. Two main ideas are involved in the proof. The first is that a holomorphic function defined in a neighborhood 'grows like a polynomial'. This is illustrated in a key inequality that we prove in our paper. The second concerns with the commutators of Toeplitz operators. The idea of localization is throughout our argument.

Oct 10

Applied Math Seminar- Dane Taylor, University at Buffalo
3:45PM, Tue Oct 10 2017, Math 250

Oct 10

Graduate Mentoring Seminar- Dr. Adam Sikora
"Math on the web and math computing".
5:00PM, Tue Oct 10 2017, Math 250

Title: "Math on the web and math computing".

Oct 11

Analysis Seminar- Jianchao Wu, Penn State University
Dimensions in topological dynamics and crossed product C*-algebras
4:00PM, Wed Oct 11 2017, Math 250

C*-algebras are a kind of operator algebras that are tailored to describe noncommutative (i.e., quantum) topological spaces through analytical means. A major and rich source of C*-algebras lies in the construction of crossed products from topological dynamical systems, which has occupied a central position throughout the history of C*-algebra theory. On the other hand, the dimension theory of C*-algebras, which studies analogs of classical dimensions for topological spaces, is young but has been gaining momentum lately thanks to the pivotal role played by the notion of finite nuclear dimension in the classification program of simple separable nuclear C*-algebras. The convergence of these two topics leads to the question: When does a crossed product C*-algebra have finite nuclear dimension? I will present some recent work on this problem.

Oct 17

Applied Math Seminar- Xudan Luo, UB
3:45PM, Tue Oct 17 2017, Math 250

Oct 18

Analysis Seminar- Kate Juschenko, Northwestern University
Cycling amenable groups and soficity
4:00PM, Wed Oct 18 2017, Math 250

I will give introduction to sofic groups and discuss a possible strategy towards finding a non-sofic group. I will show that if the Higman group were sofic, there would be a map from Z/pZ to itself, locally like an exponential map, satisfying a rather strong recurrence property. The approach to (non)-soficity is based on the study of sofic representations of amenable subgroups of a sofic group. This is joint work with Harald Helfgott.

Oct 23

Algebra Seminar-Kirill Zainoulline, University of Ottawa
Equivariant algebraic oriented cohomology and their applications
4:00PM, Mon Oct 23 2017, Math 250

We give an overview on recent developments in the study of algebraic oriented theories and their equivariant analogues (e.g. various K-theories, algebraic cobordism). We discuss various connections and applications to generalized Schubert calculus. This is based on several joint projects with B. Calmes and C. Zhong.

Oct 24

Applied Math Seminar- Matthew J. Hoffmann, Rochester Institute of Technology
3:45PM, Tue Oct 24 2017, Math 250

Oct 30

Algebra Seminar- Henry Tucker, University California, San Diego
Title:Fusion categories and their invariants
4:00PM, Mon Oct 30 2017, Math 250

The objects in fusion categories generalize complex
representations for finite groups. In particular, they are semisimple
tensor categories whose objects have duals. These categories arise
from the representation theory of a diverse range of objects, most
notably in Drinfel’d’s theory of quantum groups and Jones’s theory of
Murray-von Neumann factors. The problem of classifying fusion
categories whose tensor product has a given ring structure is the
central question of this talk. The answer to this question even for
rings that are very close to group algebras is very difficult. We
will survey the existing answers to this question; successful
approaches have highlighted the importance of tools brought over from
the theory of finite groups, including group cohomology and
Frobenius-Schur indicators.

Nov 1

Association for Women in Mathematics(AWM) Lecture Series- Dr. Aude Hofleitner, Data Scientist, Facebook
Developing Large Scale Models at Facebook
12:00PM, Wed Nov 1 2017, Hochstetter 114

In this talk I will show how data scientists leverage the Facebook infrastructure to better understand people and their connections to each other and the world. This is key to provide a personalized and meaningful experience online. I will present how we develop large scale inferences and graph mining algorithms which scale on the Facebook graph.

Bio: Aude is data science manager in the Core Data Science team, where she leads the Graph & Identity Research team. Her interest lies in the development of novel large scale inferences algorithms and statistical methodologies focusing on large scale graph inferences, graph matching and clustering which can be deployed to improve products across Facebook. Before joining Facebook, she studied for a M. Sc in Applied Math at Ecole Polytechnique and in Transportation at the Ecole des Nationale des Ponts et Chaussées. She obtained her PhD in Electrical Engineering and Computer Science (Controls & Machine Learning) at UC Berkeley.

Nov 8

Analysis Seminar- Alexandru Chirvasitu, UB
Rigidity and softness for discrete quantum groups
4:00PM, Wed Nov 8 2017, Math 250

Discrete quantum groups are the noncommutative geometer's analogue of ordinary groups, and are defined mathematically as Hopf algebras satisfying a suite of conditions that ensure they in many ways resemble group algebras of (plain) discrete groups.

In this talk I will mention various geometric and representation-theoretic concepts that transport over from discrete group theory to its quantum analogue. These include properties that seem to suggest the discrete quantum group is ``rigid'' (such as Kazhdan's property (T)) or, at the other extreme, ``soft'' (residual finiteness, soficity, etc.). The main results indicate various ways in which these properties interact.

(partly joint with Angshuman Bhattacharya, Michael Brannan and Shuzhou Wang)

Nov 13

Algebra Seminar- Yuanlin Li, Brock University
Reversible Group Rings Over Commutative Rings
4:00PM, Mon Nov 13 2017, Math 250

Let R be an associative ring with identity. R is called
reversible if ab=0 implies ba=0, and it is called symmetric if abc=0
implies acb=0 for all a,b,c in R. The reversibility property, a
natural generalization of commutativity, has been exploited by various
authors over the years; but apparently the name was introduced by Cohn
in 1999, who noted that the K\"{o}the conjecture holds for the class
of reversible rings. In this talk we present some recent results on
reversible group rings and we also mention a few open problems.

Nov 14

Applied Math Seminar- Sonjoy Das, University at Buffalo, Mechanical & Aerospace Engineering
3:45PM, Tue Nov 14 2017, Math 250

Nov 20

Algebra Seminar- Joseph Hundley, University at Buffalo
Functorial Descent and other applications of Fourier Coefficients
4:00PM, Mon Nov 20 2017, Math 250

Functorial descent is a method of constructing automorphic representations of smaller groups from representations of bigger groups, to provide a partial inverse to (nonsurjective) functorial liftings (constructed in some cases, conjectured in many others by Langlands). The method makes use of certain "Fourier coefficient maps" attached to embeddings of sl_2 into the Lie algebra of the group in question. These maps also have local field and finite field analogues and are of some interest in their own right. I will attempt to sketch the general picture and describe past and current work of mine (joint with David Ginzburg, Eitan Sayag, and Baiying Liu) in this area.

Nov 22

Start of Fall Recess
Wednesday, November 22, 2017

Nov 27

Classes Resume
Monday, November 27, 2017

Nov 28

Applied Math Seminar
Katharine Anderson, Carnegie Mellon University
3:45PM, Tue Nov 28 2017, Math 250

Nov 30

Department Faculty Meeting
4:00PM, Thu Nov 30 2017, Math 250

Dec 8

Last Day of Classes
Friday, December 8, 2017

Dec 9

Reading Days
Saturday, December 9, 2017

Dec 10

Reading Days
Sunday, December 10, 2017

Dec 11

Start of Final Exams
Monday, December 11, 2017

Dec 18

Algebra Seminar-Manuel Reyes, Bowdoin College
Toward a functorial quantum spectrum for noncommutative algebras
4:00PM, Mon Dec 18 2017, 250 Math Bldg

What kind of ``quantum space'' should play the role of the spectrum of a noncommutative algebra? Potential solutions to this problem might include a topological space, a sheaf of rings, or a noncommutative algebra of ``discrete'' functions. I will discuss various obstructions to these approaches in both ring theory and operator algebra. Then I will report on work-in-progress toward coalgebras as a ``quantum spectrum,'' yielding a potential solution to this problem in the restricted context of noetherian affine PI algebras.

Dec 19

Winter Recess Begins
Tuesday, December 19, 2017

Jan 25

Classes Begin
Monday, January 25, 2016

Feb 1

Algebra Seminar
Henry Kim(University of Toronto)
Ikeda type lift for the exceptional group of type E_7
4:00PM, Mon Feb 1 2016, Math 250

Ikeda constructed a cusp form on Sp_{2n} (rank 2n) from Hecke
eigenform on the upper half plane which has been conjectured by Duke and
Imamoglu and Ibukiyama. We give a similar construction on the 27-dimensional exceptional tube
domain where the exceptional group of type E_7 acts. This is a joint work with T. Yamauchi.

Feb 4

Faculty Meeting
4:00PM, Thu Feb 4 2016, Math 250

Feb 15

Algebra Seminar- Raul Gomez (Cornell University)
A GIT approach to Stiefel Harmonics
4:00PM, Mon Feb 15 2016, Math 250

In 1974, Stephen Gelbart developed a theory of Stiefel harmonics for the Stiefel manifolds $SO(n)/SO(n-m)$ generalizing, in this way, the theory of spherical harmonics. (That is, the case $m=1$.) This theory has been further extended to include compact Stiefel manifolds of Unitary and Symplectic type. In this talk we describe a new, unified, approach to Stiefel harmonics using Geometric Invariant Theory. Time permitting, I will also explain some directions of further research that can be taken with this approach.

This is an outgrowth of the Cornell SPUR summer program.

Feb 16

Applied Mathematics Seminar- Gregor Kovačič, Rensselaer Polytechnic Institute
Firing-Rate Model of Neuronal Networks
4:00PM, Tue Feb 16 2016, Math 250

The firing-rate model has long been used as a tool for simplifying descriptions of neuronal network dynamics and uncovering plausible underlying physiological mechanisms. This talk will review some of our recent work on such models, with connections to modeling information compression in sensory pathways and insect olfaction.

Feb 16

Graduate Mentoring Seminar- Dr. Joseph Hundley
Representation theoretic methods in automorphic forms
5:00PM, Tue Feb 16 2016, Math 250

We give a brief introduction to the subject of automorphic forms, representations, and L-functions, beginning with the simplest examples (holomorphic modular forms on the upper half plane) and progressing to computational aspects of pushing classical ideas into exceptional groups.

Feb 18

Colloquium- Erkao Bao (UCLA)
An invitation to contact homology.
4:00PM, Thu Feb 18 2016, Math 250

Contact homology is an invariant of a contact structure. In this talk, we will start with the definition of a contact structure, then build up our way by looking at the Morse homology, and finally we will have a gentle definition of contact homology, which can be viewed as an infinite dimensional Morse homology.

Feb 19

Geometry/Topology Seminar- Erkao Bao (UCLA)
Semi-global Kuranishi structures and contact homology.
4:00PM, Fri Feb 19 2016, Math 122

Contact homology was proposed and studied by Eliashbergy, Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until last year.
In this talk, we will first see that the naive definition does not work because the spaces of "trajectories" that we count to define the differential of contact homology are not transversally cut out. Then we will construct a finite dimensional space K around the spaces of "trajectories" in a systematical way, and inside K we perturb the "trajectories" so that now they are transversally cut out. The space K together with the perturbation is called a semi-global Kuranishi structure.

Feb 23

Graduate Mentoring Seminar-Fred Stoss
Library Research Skills for Graduate Students
5:00PM, Tue Feb 23 2016, Math 250

Finding important and information is an integral part of scholarly research. It is a skill that increases knowledge, understanding, and productivity in the classroom, in the laboratory, in the field, in the office, and in any setting where precise information is needed. These are fundamental skills last well beyond a student’s stay at UB. Graduate students (as well as upper-division undergraduate students and others interested parties) at UB have many things to master. One of them is effective and efficient navigation of the UB Libraries’ services, collections, and expertise in locating relevant resources in support of your research and classroom activities. Assignments may require preparing a paper, report, presentation, extra-credit or other projects and presentations. Librarians teach research processes, tips, and hints for finding the appropriate databases, journal articles, technical report, reference books, and other resources—and how to effectively, efficiently, and economically (think in terms of savings in time). Scholarly and academic journal articles, trade and current news, books and technical reports, patents, high-quality Websites, and dissertations and theses are important tools in your “Math Student’s Tool Kit.” This presentation describes major library tools with which you build your library research skills—finding databases, articles, books, reference resources, and library workshops teaching the basics for students—by developing efficient and effective strategies identifying information resources in and through the University Libraries.

Feb 24

Analysis Seminar
Lewis Coburn (SUNY at Buffalo)
Toeplitz quantization on the Fock space and Lipschitz approximation
4:00PM, Wed Feb 24 2016, Math 250

Title: Toeplitz quantization on the Fock space and Lipschitz approximation

Feb 26

Geometry/Topology Seminar- Hans Boden (McMaster Univ.)
“A classical approach to virtual knots”
4:00PM, Fri Feb 26 2016, Math 122

Given a virtual knot K, there are various groups naturally associated to K, including the analogue of classical knot group G_K, the virtual knot group VG_K, the extended knot group EG_K (Silver-Williams), and the quandle group QG_K (Manturov). Each group occurs as the quotient of VG_K in a natural way, and we introduce Alexander-line invariants derived from it using elementary ideal theory. For instance, associated to the k=0 ideal of the virtual knot group VG_K is a polynomial H_K(s,t,q) in three variables, and we show how the q-width of H_K gives information about the virtual crossing number of K. The polynomial H_K(s,t,q) satisfies a skein formula, and one can define a twisted polynomial invariant of virtual knots for any representation from VG_K to GL_n(R).

Feb 29

AWM Lecture Series-Dr. Alyssa Thompson(National Security Agency)
A Look at the Crypt at the NSA, An Overview of Public Key Cryptography
5:00PM, Mon Feb 29 2016, Math 250

Title: A Look at the Crypt at the NSA, An Overview of Public Key Cryptography

As a mathematician at the National Security Agency, I get to do a lot of interesting math. I
work in an office called cryptography in systems which develops new cryptography. Although I can't share any of the details of my work, I'm instead going to give an overview of public key cryptography and what it looks like in the past, present and future. I will also talk a little about NSA, what it's like to work there and some job opportunities for mathematicians.

Mar 1

Graduate Mentoring Seminar- Dr. Hanfeng Li
What is a sofic group?
5:00PM, Tue Mar 1 2016, Math 250

The class of sofic groups was introduced by Gromov in 1999, and has received a lot of attention since then. I will explain the definition of sofic groups and its connection to various other fields such as dynamical systems, ring theory and L2-invariants theory.

Mar 2

Analysis Seminar
Zhengxin Lian (University of Science and Technology of China and SUNY at Buffalo)
Sequences realized by noncommutative toral automorphisms with zero entropy and Sarnak conjecture
4:00PM, Wed Mar 2 2016, SUNY at Buffalo

http://www.math.buffalo.edu/~hfli/abstract-Spring 2016-Lian.pdf

Mar 4

Geometry/Topology Seminar- Laurent Siebenmann(Université de Paris-Sud)
Towards a more geometric understanding of planar flows.
4:00PM, Fri Mar 4 2016, Math 122

Concerning an oriented foliation F of the plane R^2 by the
orbits of a given nowhere-singular flow on R^2, there is a
risky conjecture that seems of interest. It involves T the
universal Hausdorff quotient of the (usually non-Hausdorff)
leaf space LF of F. This T is known to be in the class of
trees that are coherently oriented, metrizable, separable,
having only countably many branch points, and having no
extremal points. Call such a tree admissible. The preimages in
R^2 of the branch points of T are the so-called Conley
pseudo-leaves of F, each of which is a countable union of Reeb
pseudo-leaves of F.

The conjecture asserts that there is a natural continuous and
surjective "classifying map" f: D^2 --> T+, of a 2 disk D^2
compactifying R^2, onto an end compactification T+ of T, such
that the connected components of the point preimages of the
restriction of f to the interior R^2 of D^2 is the foliation F.

I have studied a class of closed submanifolds-with-boundary in
R^2 that are foliated by F. This has led me to a pleasant proof of a
variant of Mather's compactification theorem and also to some
progress on the risky conjecture. In particular, I will
indicate how the conjecture can hopefully be proved in case
the set of branch points in T is locally finite.

Mar 7

Algebra Seminar- Dorian Goldfeld (Columbia University)
An additive function that counts prime divisors
4:00PM, Mon Mar 7 2016, Math 250

Every integer n > 1 has a unique factorization into prime powers. Alladi and Erdos introduced the additive function A(n) which is the sum of the primes dividing n (counting multiplicity). Here additive function means A(mn) = A(m) + A(n). We will show that A(n) is uniformly distributed among arithmetic progressions.

Mar 14

Spring Recess
Monday, March 14, 2016

Mar 21

Classes Resume
Monday, March 21, 2016

Mar 21

Algebra Seminar- Xueqing Chen (University of Wisconsin)
Hall algebras over triangulated categories
4:00PM, Mon Mar 21 2016, Math 250

Hall algebras provided a framework involving the categorification and the geometrization of Lie algebras and quantum groups. One can use hall algebras over Abelian categories and triangulated categories to realize quantum groups and Kac-Moody algebras. In this talk, the constructions of Hall algebras of some orbit triangulated categories via derived Hall algebras for derived categories will be presented and the relations between them will be characterized. Especially, inspired by the recent work of Bridgeland, we construct extended derived Hall algebras over 2-periodic derived categories in order to realize the quantum groups globally. Another application will be a natural algebra homomorphism from the Ringel-Hall algebra of a hereditary algebra to the corresponding quantum cluster algebra, which gives alternative proofs of some results recently obtained by Berensein and Rupel. This talk is based on joint works with Ming Ding, Fan Xu and Jie Xiao.

Mar 28

Algebra Seminar- Solomon Friedberg (Boston College)
Automorphic Forms for Covering Groups (Sol Friedberg, Boston College)
4:00PM, Mon Mar 28 2016, Math 250

The double cover of the symplectic group, the so-called metaplectic group, was introduced by Weil in explaining the behavior of the Jacobi theta function and its generalizations. However, there is a much broader class of covering groups that are tied to arithmetic in their very construction. In this talk I describe aspects of the theory of automorphic forms on these covering groups, including the construction of higher theta functions and of L^2 functions whose Fourier coefficients are related to Gauss sums. Doing so makes use of the descent method. This is based on joint work with David Ginzburg.

Apr 1

Colloquium- Chad Giusti (University of Pennsylvania)
Neural networks and the nerve theorem
2:00PM, Fri Apr 1 2016, Math 250

In practice, many of the most successful models of abstract neural networks or the function of brain systems are constructed on a foundation of convex geometry, often without the knowledge of those using or constructing the models. Our initial attempts to develop theory about the coding properties such modeled systems has revealed deep connections to fundamental notions from algebraic geometry and topology. In this talk, I will describe some of these connections, give an outline of what we already know as a result of these connections, and describe a number of interesting open mathematical problems that we've found along the way. No knowledge of neuroscience is assumed.

Apr 4

Algebra Seminar- Jack Buttcane (SUNY Buffalo)
GL(3) Kloosterman sums and spectral large sieve inequalities
4:00PM, Mon Apr 4 2016, Math 250

The spectral large sieve inequalities give a very strong trivial bound when studying spectral averages of L-functions. They are related to bilinear forms in certain generalized Kloosterman sums through the Kuznetsov formula. I will discuss the role of the spectral large sieve inequalities on GL(2), then on GL(3) I will give a decomposition of the Kloosterman sums into classical Kloosterman sums and show how this leads to near-optimal bounds on the bilinear forms and then to optimal bounds for the large sieve inequalities.

Apr 5

Applied Math Seminar- David Salac (Department of Mechanical and Aerospace Engineering) (MAE), UB
"Recent advances in the modeling of vesicles in electric or magnetic fields"
4:00PM, Tue Apr 5 2016, Math 250

Vesicles undergo interesting dynamics when exposed to electric or magnetic fields. Electric fields induce large deformation in the vesicle membrane and induce movement of lipid membrane domains. Alignment of vesicles in magnetic fields have also been demonstrated. Here, a recent numerical model of vesicles is presented that allows for the investigation of the electrohydrodynamics of mono- and multi-component vesicles in addition to the magnetohydrodynamics of vesicles. The model uses an improved level set method coupled to a novel Navier-Stokes projection method which enforces local and global volume and surface area conservation. The model, sample results, and possibilities for future work will be outlined.​

Apr 5

Graduate Mentoring Seminar- Dr. David Hemmer
“An introduction to representation theory.”
5:00PM, Tue Apr 5 2016, Math 250

“An introduction to representation theory.”

Apr 6

Analysis Seminar
Timothy Rainone (University of Waterloo)
K-theoretic dynamics and the C*-Connes embedding problem
4:00PM, Wed Apr 6 2016, Math 250

http://www.math.buffalo.edu/~hfli/abstract-Spring2016-Rainone.pdf

Apr 11

Algebra Seminar-Eyal Kaplan (Ohio State University)
Doubling global constructions for tensor product L-functions
4:00PM, Mon Apr 11 2016, Math 250

Title: Doubling global constructions for tensor product L-functions

I will present a joint work with Cai, Friedberg and Ginzburg. In a series of constructions, we apply the "doubling method" from the theory of automorphic forms to covering groups. We obtain partial tensor product L-functions attached to generalized Shimura lifts, which may be defined in a natural way since at almost all places the representations are unramified principal series.

Apr 12

This Talk has been postponed/rescheduled for April 19, 2016 Graduate Mentoring Seminar- Dr. Li Wang
"Introduction to multiscale modeling and computation"
5:00PM, Tue Apr 12 2016, Math 250

In this talk, I will give two specific examples on how to model problems with multiple scales: one on human crowds in panic situations and the other on viscous thin film flow laden with particles down an incline. On the computational side, I will focus on the domain decomposition method and asymptotic preserving method, and explain the main ideas through a toy model.

Apr 13

Analysis Seminar
Ilijas Farah (York University)
A new bicommutant theorem
4:00PM, Wed Apr 13 2016, Math 250

I'll prove an analogue of Voiculescu’s theorem: Relative bicommutant of a separable unital subalgebra A of an ultraproduct of simple unital C*-algebras is equal to A.

Apr 14

Colloquium- Dr. Hung P. Tong-Viet (Kent State University)
Derangements in primitive permutation groups and applications
4:00PM, Thu Apr 14 2016, Math 250

A derangement (or fixed-point-free permutation) is a permutation with no fixed points. One of the oldest theorems in probability, the Montmort limit theorem, says that the proportion of derangements in finite symmetric groups Sn tends to 1/e when n tends to infinity. A classical theorem of Jordan implies that every finite transitive permutation group of degree greater than 1 contains derangements. This result has many applications in number theory, topology, game theory, combinatorics, and representation theory. There are several interesting questions on the number and the order of derangements that have attracted much attention in recent years. In this talk, I will discuss some of these questions
and I will report on recent results on finite primitive permutation groups with some restriction on derangements (joint with T.C. Burness) and some application to modular representation theory (joint with M.L. Lewis).

Apr 19

Graduate Mentoring Seminar- Dr. Li Wang
"Introduction to multiscale modeling and computation"
5:00PM, Tue Apr 19 2016, Math 250

In this talk, I will give two specific examples on how to model problems with multiple scales: one on human crowds in panic situations and the other on viscous thin film flow laden with particles down an incline. On the computational side, I will focus on the domain decomposition method and asymptotic preserving method, and explain the main ideas through a toy model.

Apr 22

Geometry/Topology Seminar-Juanita Pinzon-Caicedo (U. of Georgia)
An Overview of Relative Trisections.
4:00PM, Fri Apr 22 2016, Math 122

A trisection of closed 4—manifold is a decomposition of a 4—manifold into three copies of $\natural^k S^1\times B^3$, that intersect pairwise in 3--dimensional handlebodies, and with triple intersection a 2--dimensional surface. Relative trisections are a generalization of a trisection to include 4--manifolds with boundary. In the talk I will present the basics of relative trisections starting with their relationship to open book decompositions of the bounding manifolds. I will then introduce a stabilization operation that gives rise to a statement about the uniqueness of relative trisections, thus complementing Gay and Kirby's proof of the existence of relative trisections. Finally, I will introduce the notion of diagrams of relative trisections and describe a method to recover the open book decomposition of the bounding manifold from the trisection diagrams.

Apr 28

Applied Math Seminar Dr. Fengyan Li -Rensselaer Polytechnic Institute (RPI)
On Discontinuous Galerkin Methods for 1d Wave Equations
4:00PM, Thu Apr 28 2016, Math 250 -

Discontinuous Galerkin (DG) methods have been widely used in wave
simulations due to their excellent dispersive and dissipative
properties. In this work, we will examine some theoretical aspects of
the methods when they are applied to 1d two-way wave equations. Here a
general family of L2 stable DG methods will be considered for their
stability, accuracy, and dispersion properties. A sub-family of the
methods is further identified that is optimal in L2 errors and displays
some superconvergence property. New insight is provided into some known
observations when DG methods are applied to wave equations.

May 5

Department Faculty Meeting
4:00PM, Thu May 5 2016, Math 250

May 6

Last Day of Classes
Friday, May 6, 2016

May 9

Semester Final Examinations
Monday, May 9, 2016

May 13

Commencement Weekend
Friday, May 13, 2016

May 31

Summer Session "J" Begins
Tuesday, May 31, 2016

Jul 8

Summer Session "J" Ends
Friday, July 8, 2016

Jul 11

Summer Session "M" Begins
Monday, July 11, 2016

Aug 19

Summer Session "M" ends
Friday, August 19, 2016

Aug 29

Fall Classes Begin
Monday, August 29, 2016

Sep 2

G&T Seminar
Organizational meeting
4:00PM, Fri Sep 2 2016, Math 122

Sep 5

Labor Day Observed (no classes)
Monday, September 5, 2016

Sep 6

Graduate Mentoring Seminar- Dr. William Menasco
"Menasco's Rules for Doing Research."
5:00PM, Tue Sep 6 2016, Math 250

"Menasco's Rules for Doing Research."

Sep 13

Graduate Mentoring Seminar-Dr. Bernard Badzioch
"Using LaTeX"
5:00PM, Tue Sep 13 2016, Math 250

"Using LaTeX"

Sep 16

G&T Seminar
Erkao Bao (UCLA)
Definition of cylindrical contact homology in dimension three
4:00PM, Fri Sep 16 2016, Math 122

Cylindrical contact homology is an invariant of contact structures of certain contact manifolds. In this talk I will give a rigorous and relatively easy definition of cylindrical contact homology in dimension three using obstruction bundle calculations. In particular, it does not use virtual techniques, such as semi-global Kuranishi structures.

Sep 20

Graduate Mentoring Seminar- Dr. William Menasco
"Documenting Your Achievements."
5:00PM, Tue Sep 20 2016, Math 250

"Documenting Your Achievements."

Sep 23

G&T Seminar
Elizabeth Munch (Albany)
The interleaving distance
4:00PM, Fri Sep 23 2016, Math 122

When working with data, it is imperative to have a definition of a distance in order to rigorously define concepts such as noise and approximations. The interleaving distance was first defined in the context of generalizing the bottleneck distance for persistence diagrams, a common tool from topological data analysis (TDA) by Chazal et al. It was then shown to fit easily into the cateogirified framework of persistence modules provided by Bubenik and Scott. Category theory allows the idea to be fludily moved and redefined to work on many other constructions. In particular, some standard metrics such as $L_\infty$ and Hausdorff distance, can also be viewed as special cases of the interleaving distance. In this talk, we will discuss the basic ideas for the interleaving, its generalized definition in the category theory langugage, and recent work extending this idea to give interleavings on Reeb graphs and Merge trees.
This work is joint with Vin de Silva, Amit Patel, and Anastasios Stefanou.

Sep 26

Algebra Seminar- Chun-Ju Lai, Max Planck Institute for Mathematics
Affine Hecke algebras and quantum symmetric pairs
4:00PM, Mon Sep 26 2016, Math 250

One breakthrough in the theory of quantum groups is the construction of the canonical bases.
For type A, there is a geometric construction for the (idempotented) quantum group together with a canonical basis due to Beilinson, Lusztig and MacPherson via flag varieties and dimension counting. An algebraic approach is also available via Heckle algebras and its combinatorics.
In this talk I will present our work on the generalization to affine type C using the Hecke algebraic approach, in which several new phenomenons have been observed. I will also talk about the related quantum symmetric pairs.

This is a joint work with Z.~Fan, Y.~Li, L.~Luo, and W.~Wang.

Sep 27

Graduate Mentoring Seminar- Dr. David Hemmer
An Introduction to Mathematical Publishing for graduate students.
5:00PM, Tue Sep 27 2016, Math 250

An Introduction to Mathematical Publishing for graduate students.

Oct 4

Applied Math Seminar-Alethea Barbaro (Case Western)
A Phase Transition in a Model for Gang Territorial Development
4:00PM, Tue Oct 4 2016, Math 250

Spray-painting a gang's graffiti around the neighborhood is a job which is often relegated to the youngest members of the gang. However, this is one of the main ways for a gang to lay claim to an area. In this talk, we examine a model for territorial development based on this mechanism. We employ an agent-based model for two gangs, where each agent puts down graffiti markings and moves to a neighboring site, preferentially avoiding areas marked by the other gang. We observe numerically that the systems undergoes a phase transition from well-mixed to segregated territories as the intensity of the avoidance of the other gang's graffiti is varied. We then derive a system of macroscopic PDEs from the model and examine the phase transition in the context of the continuum system.​

Oct 4

Graduate Mentoring Seminar- Fred Stoss
Library Research Skills for Math Graduate Students.
5:00PM, Tue Oct 4 2016, Math 250

Library Research Skills for Math Graduate Students.

Oct 7

Algebra Seminar- Professor Du Jie, University of New South Wales, Australia
q-Schur algebras and their affine and super counterparts
3:00PM, Fri Oct 7 2016, Math 122

Schur algebras are certain finite dimensional algebras introduced by Issai Schur, one of the pioneers of representation theory, at the beginning of last century to relate representations of the general linear and symmetric groups. This theory is also known as the Schur-Weyl duality. Over its history of more than one hundred years, Schur algebras continue to make profound influence in several areas of mathematics such as Lie theory, representation theory, invariant theory, combinatorics, etc. I will outline some definitions of (quantum) Schur algebras and discuss a number of applications. In particular, I will report on some latest developments in the affine and super cases.

Oct 10

Jieru Zhu, University of Oklahoma
Presenting cyclotomic Schur algebras
4:00PM, Mon Oct 10 2016, Math 250

A classical result states that the action of $\mathfrak{gl}(V)$ and the symmetric group on $d$ letters mutually centralize each other on the $d$-fold tensor of $V$. If $V$ admits an action by $\mathbb{Z}/r\mathbb{Z}$, it induces an action of the wreath product of Z/rZ and the symmetric group on $d$ letters. A Levi Lie subalgebra $\mathfrak{g}$ of $\mathfrak{gl}(V)$ gives the full centralizer of this action, and we further showed a presentation for the cyclotomic Schur algebra. This provides a PBW type basis and a second presentation for the Schur algebra with idempotent generators. Same is true in the quantum setting, where the centralizer of the Ariki-Koike algebra admits similar presentations. When $r=2$, this becomes to the Type B hyperoctahedral Schur algebra defined by Richard Green.

Oct 11

Graduate Mentoring Seminar-Dr. Adam Sikora
Math and Computers.
5:00PM, Tue Oct 11 2016, math 250

Math and Computers.

Oct 13

Tenured faculty meeting
4:00PM, Thu Oct 13 2016, Math 250

Oct 17

Algebra Seminar- Michiel Kosters, University of California, Irvine
On the arithmetic of Z_p-extensions.
4:00PM, Mon Oct 17 2016, Math 250

Let ... C_i -- ... -- C_2 -- C_1 -- C_0 be a Z_p-cover of
curves over a finite field k of characteristic p. In this talk we will
discuss when the genus of C_i is a polynomial in p and i when C_0 is the
projective line. To answer this question, we will first describe all
Z_p-extensions of any field K of characteristic p. We will then use
class field theory, in particular the so-called Schmid-Witt symbol, to
compute the genus of the curves in Z_p-towers over the projective
line.

Oct 18

Myhill Lecture Series -Gopal Prasad
4:00PM, Tue Oct 18 2016, Math 250

Oct 19

Myhill Lecture Series -Gopal Prasad
4:00PM, Wed Oct 19 2016, Math 250

Oct 20

Myhill Lecture Series -Gopal Prasad
4:00PM, Thu Oct 20 2016, Math 250

Oct 21

G&T Seminar
Tarik Aougab (Brown)
Hyperbolic subspaces and super-polynomial divergence
4:00PM, Fri Oct 21 2016, Math 122

There are several useful properties satisfied by geodesics in negatively curved spaces, including the classical Morse lemma, which states that if p is any relatively efficient path with endpoints on the geodesic, then p must lie in a bounded neighborhood of the geodesic. In other words: there are no efficient paths connecting points on the geodesic that drift far away from the geodesic. We will discuss several related properties, including "super-linear divergence" for geodesics in negatively curved spaces, and we prove that all of these properties are actually equivalent in great generality: a geodesic in an arbitrary (not necessarily hyperbolic or negatively curved) geodesic metric space satisfies one of these properties if and only if it satisfies all of them. We use this equivalence to study hyperbolic extensions of surface groups, free groups, and certain hyperbolic subgroups of relatively hyperbolic groups. This represents joint work with Matthew Durham and Samuel Taylor.

Oct 24

Algebra Seminar- Gufang Zhao, University of Massachusetts, Amherst.
Cohomological Hall algebras and quantum groups
4:00PM, Mon Oct 24 2016, Math 250

This talk is based on my joint work with Yaping Yang. We use ideas from enumerative geometry and stable homotopy theory to study quantum groups and their representations. I will talk about a geometric construction of quantum group associated to each quiver Q and each oriented cohomology theory A. The construction uses cohomological Hall algebras of Nakajima quiver varieties. I will focus on two examples. 1. when A is the Morava K-theory, we obtain a family of new quantum groups, linking complex representations to modular representations of a Lie algebra. 2. when A is the equivariant elliptic cohomology, we establish a sheafified elliptic quantum group for any symmetric Kac-Moody Lie algebra, rational sections of which gives the algebra of elliptic R-matices, and algebra structure of which is related to the factorization structure on affine Grassmannian over an elliptic curve.

Oct 31

Algebra Seminar- Chad Mangum, Niagara University
Fermionic Representations of Twisted Toroidal Lie Algebras
4:00PM, Mon Oct 31 2016, Math 250

Lie algebra representation theory has been significant in various areas of mathematics and physics for several decades. In this talk, we will discuss one instance of this theory, namely certain representations of twisted (2-)toroidal (Lie) algebras, which we view as universal central extensions of twisted multi-loop algebras. The usual loop algebra realization generalizes the familiar realization of affine Kac-Moody algebras. To facilitate our study of the representation theory, however, we will discuss a new realization given by generators and relations; this is similar to a realization by Moody, Rao, and Yokonuma in the untwisted case. Subsequently, we will discuss an application, namely fermionic free field representations, which are similar to those of Feingold and Frenkel in the case of affine algebras. If time permits, we will compare these results to other recent work by the authors. This is joint work with Kailash Misra and Naihuan Jing.

Nov 3

Tenured Faculty Meeting
4:00PM, Thu Nov 3 2016, Math 250

Nov 4

G&T Seminar
Bulent Tosun (Alabama)
Obstructing pseudo-convex embeddings of Brieskorn spheres into complex 2-space
4:00PM, Fri Nov 4 2016, Math 122

A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure? In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related conjecture of Gompf, which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold (This is joint work with Tom Mark.)

Nov 10

Applied Math Seminar- Pavel Lushnikov, University of New Mexico
4:00PM, Thu Nov 10 2016, Math 250

Nov 15

Applied Math Seminar- Misun Min (Argonne National Lab)
4:00PM, Tue Nov 15 2016, Math 250

Nov 23

Start of Fall Recess
Wednesday, November 23, 2016

Nov 28

Classes Resume
Monday, November 28, 2016

Nov 28

Algebra Tenure Track Job Talk
TBA
4:00PM, Mon Nov 28 2016, Math 250

TBA

Nov 29

Algebra Tenure Track Job Talk
TBA
4:15PM, Tue Nov 29 2016, Math 250

TBA

Nov 30

Algebra Tenure Track Job Talk
TBA
4:00PM, Wed Nov 30 2016, Math 250

TBA

Dec 1

Algebra Tenure Track Job Talk
TBA
4:00PM, Thu Dec 1 2016, Math 250

TBA

Dec 2

G&T Seminar
Jeremy Van Horn-Morris (Arkansas)
Incorporating genus into the Heegaard Floer differential
4:00PM, Fri Dec 2 2016, Math 122

Utilizing work of Hutchings and Kutluhan-Lee-Taubes, one can incorporate the genus of holomorphic curves into the Heegaard Floer differential of the Honda-Kazez-Matic description of the Heegaard Floer complex associated to an open book decomposition. We will describe how this can be used to define a version of the Oszvath-Szabo contact invariant that is more sensitive both to tightness and to Stein cobordisms. This is joint work with Cagatay Kutluhan, Gordana Matic and Andy Wand.

Dec 5

Applied Tenure Track Job Talk-Amy Cochran, University of Michigan
Mathematical Classification of Bipolar Disorder
4:00PM, Mon Dec 5 2016, Math 250

Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence. In this talk, I present patient-specific models of mood in bipolar disorder that incorporate existing longitudinal data. In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions. I show that this model accurately describes the data and that it can be personalized to an individual. Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.

Dec 6

Applied Tenure Track Job Talk
TBA
4:00PM, Tue Dec 6 2016, Math 250

TBA

Dec 8

Algebra Tenure Track Job Talk
TBA
4:00PM, Thu Dec 8 2016, Math 250

TBA

Dec 9

Last Day of Classes
Friday, December 9, 2016

Dec 9

Applied Tenure Track Job Talk
TBA
4:00PM, Fri Dec 9 2016, Math 150

TBA

Dec 10

Reading Days
Saturday, December 10, 2016

Dec 11

Reading Days
Sunday, December 11, 2016

Dec 12

Start of Final Exams
Monday, December 12, 2016

Dec 12

Applied Tenure Track Job Talk
TBA
4:00PM, Mon Dec 12 2016, Math 250

TBA

Dec 20

Winter Recess Begins
Tuesday, December 20, 2016