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
