Apr 26

Tenured faculty meeting
4:00PM, Thu Apr 26 2018, 250 Math Bldg.

May 4

G&T Seminar
Angelica Deibel (Brandeis)
Random Coxeter groups
4:00PM, Fri May 4 2018, 122 Math

Random right-angled Coxeter groups have been studied extensively using methods and results from random graph theory. Some of these methods can be extended to study random Coxeter groups in general. In this talk, I will introduce random Coxeter groups and give several results.

May 7

Algebra Seminar
Shizhuo Zhang, Indiana University
Exceptional collections of line bundles and quiver moduli.
4:00PM, Mon May 7 2018, 250 Mathemtics Bldg.

Let $X$ be a smooth projective surface with a so called
cyclic strong exceptional collection of line bundles, I will show that
$X$ is weak del Pezzo surface and we classify all the weak del pezzo
surfaces with such collections. Then I will show that the various
notions in different areas of mathematics are actually the same, which
answer a question posed by Ballard and Favero. Then I will talk about
the quiver moduli associated to such collections of line bundles and
show that with an appropriate stability condition $\theta$, the weak
del Pezzo surface with such collections can be realized as the quiver
moduli. This is a joint work with Xuqiang Qin.

May 9

Analysis Seminar- Rostislav Grigorchuk, Texas A&M University
Group of intermediate growth, aperiodic order, and Schroedinger operators.
4:00PM, Wed May 9 2018, 250 Math Bldg.

I will explain how seemingly unrelated objects: the group G of intermediate growth constructed by the speaker in 1980, the aperiodic order, and the theory of (random) Schroedinger operator can meet together. The main result, to be discussed, is based on a joint work with D.Lenz and T.Nagnibeda. It shows that a random Markov operator on a family of Schreier graphs of G associated with the action on a boundary of a binary rooted tree has a Cantor spectrum of the Lebesgue measure zero. This will be used to gain some information about the spectrum of the Cayley graph. The main tool of investigation is given by a substitution, that, on the one hand, gives a presentation of G in terms of generators and relations, and, on the other hand, defines a minimal substitutional dynamical system which leads to the use of the theory of random Shroedinger operator.
No special knowledge is assumed, and the talk is supposed to be easily accessible for the audience.

May 10

Faculty Meeting
4:00PM, Thu May 10 2018, Math 250

May 11

Last Day of Classes
Friday, May 11, 2018

May 11

G&T Seminar
Bill Menasco (Buffalo)
Distance and intersection number in the curve complex (Continued)
4:00PM, Fri May 11 2018, 122 Math

Let $S_g$ be a closed oriented surface of genus $g \geq 2$ and $\mathcal{C}^1(S_g)$ be its curve complex—vertices are homotopy classes of essential simple closed curves with two vertices sharing an edge if they have disjoint representatives. It is known that $\mathcal{C}(S_g)$ is path connected , and the
distance, $d(\alpha , \beta)$, between two vertices $\alpha , \beta \in \mathcal{C}^1(S)$ is just the minimal count of the number of edges in an edge-path between $\alpha$ and $\beta$. One can also consider, $ i(\alpha , \beta)$, the minimal intersection between curve representatives of $\alpha$ and $\bet$. This talk discusses how $i(\alpha , \beta)$ will grow as $d(\alpha, \beta)$ grows. This is joint work with Dan Margalit.

May 12

Reading Days
Saturday, May 12, 2018

May 13

Reading Days
Sunday, May 13, 2018

May 14

Semester Finals Begin
Monday, May 14, 2018

May 18

Commencement Weekend
Friday, May 18, 2018

Aug 27

Algebra Seminar-Ben Webster, University of Waterloo
Representation theory of symplectic singularities
4:00PM, Mon Aug 27 2018, 150 Mathematics Bldg.

There are a lot of non-commutative algebras out there in the
world, so if you want to study some of them, you have to have a theory
about which are especially important. One class I find particularly
interesting are non-commutative algebras which "almost" commutative
and thus can be studied with algebraic geometry, giving a rough
dictionary between certain non-commutative algebras and certain
interesting spaces. This leads us to a new perspective on some
well-known algebras, like universal enveloping algebras, and also to
new ones we hadn't previously considered. The representations of the
resulting algebras have a lot of interesting structure, and have
applications both in combinatorics and in the construction of knot
invariants.

Aug 30

Faculty Meeting
4:00PM, Thu Aug 30 2018, 250 Mathematics Bldg.

Sep 4

Graduate Mentoring Seminar- Dr. William Menasco

5:00PM, Tue Sep 4 2018, Math 250

"Menasco's Rules for doing mathematics."

Sep 5

Analysis Seminar- Mariusz Tobolski, Institute of Mathematics Polish Academy of Sciences
Local-triviality dimension of actions of compact quantum groups

Abstract:  "Local-triviality dimension of actions of compact quantum groups"
We introduce the local-triviality dimension of an action of a compact quantum group on a unital C*-algebra using completely positive contractive order zero maps of Winter and Zacharias. In the case of a compact Hausdorff group acting on a compact Hausdorff space our definition recovers the usual local triviality of a compact principal bundle.
Actions with finite local-triviality dimension are automatically free and there exists an analog of an n-universal bundle (in the sense of Steenrod) for any compact quantum group G. Our main motivating examples are the Matsumoto-Hopf fibration and the antipodal action on free orthogonal quantum sphere. As the main application, we prove a Borsuk-Ulam-type conjecture of Baum, Dąbrowski and Hajac in the case where the compact quantum group G admits a classical subgroup whose induced action has finite local-triviality dimension.
4:00PM, Wed Sep 5 2018, 150 Mathematics building

  "Local-triviality dimension of actions of compact quantum groups"
We introduce the local-triviality dimension of an action of a compact quantum group on a unital C*-algebra using completely positive contractive order zero maps of Winter and Zacharias. In the case of a compact Hausdorff group acting on a compact Hausdorff space our definition recovers the usual local triviality of a compact principal bundle.
Actions with finite local-triviality dimension are automatically free and there exists an analog of an n-universal bundle (in the sense of Steenrod) for any compact quantum group G. Our main motivating examples are the Matsumoto-Hopf fibration and the antipodal action on free orthogonal quantum sphere. As the main application, we prove a Borsuk-Ulam-type conjecture of Baum, Dąbrowski and Hajac in the case where the compact quantum group G admits a classical subgroup whose induced action has finite local-triviality dimension.

Sep 7

G&T Seminar
Ludwik Dąbrowski (SISSA)
The weak Hilbert-Smith conjecture from the Borsuk-Ulam type conjecture
4:00PM, Fri Sep 7 2018, 122 Math

We show that a conjecture of Ageev follows from the Borsuk-Ulam-type
conjecture of Baum, Dabrowski and Hajac. Then we explain how the Ageev
conjecture implies the weak version of the Hilbert-Smith conjecture which
states that no infinite compact zero-dimensional group can act freely on a
manifold so that the orbit space is finite dimensional. The Hilbert-Smith
conjecture originates from the already settled Hilbert's fifth problem
concerning a characterization of Lie groups.

Sep 7

Applied Math Happy Hour
5:00PM, Fri Sep 7 2018, Anchor Bar on corner of Maple and Sweethome Rd.

Sep 10

Algebra Seminar-Piotr M. Hajac, IMPAN
An equivariant pullback structure of trimmable graph c*-algebras
4:00PM, Mon Sep 10 2018, 150 Mathematics Bldg.

We prove that the graph C*-algebra C*(E) of a trimmable graph E is
U(1)-equivariantly isomorphic to a pullback C*-algebra of a subgraph
C*-algebra C*(E") and the C*-algebra of functions on a circle tensored
with another subgraph C*-algebra C*(E'). This allows us to unravel the
K-theory of the fixed-point subalgebra C*(E)^U(1) through the
(typically simpler) K-theory of C*(E'), C*(E") and C*(E")^U(1).

To obtain interesting examples of trimmable graphs, we consider
one-loop extensions of the standard graphs encoding respectively the
Cuntz algebra O_2 and the Toeplitz algebra T. Then we analyze
equivariant pullback structures of trimmable graphs yielding the
C*-algebras of the Vaksman-Soibelman quantum sphere S^{2n+1}_q and the
quantum lens space L^3_q(l;1,l), respectively.

Based on joint work with Francesca Arici, Francesco D'Andrea and
Mariusz Toboloski.

Sep 11

Graduate Mentoring Seminar-Dr. Bernard Badzioch

5:00PM, Tue Sep 11 2018, Math 250

"Using LaTeX"

Sep 12

Analysis Seminar- Jianchao Wu, Penn State University
Demystifying Rokhlin dimension and related notions
4:00PM, Wed Sep 12 2018, 150 Math Bldg

The theory of Rokhlin dimension was introduced by Hirshberg, Winter and Zacharias as a tool to study the regularity properties of C*-algebras in relation with group actions. It was inspired by the classical Rokhlin lemma in ergodic theory. Since then, it has been greatly developed as well as simplified, and connections to other areas have been discovered. In this talk, I will present some newer perspectives to help us understand this concept. In particular, I will explain its relation to the Schwarz genus for principal bundles in the context of generalized Borsuk-Ulam theorems. Time permitting, I will also indicate how one can extend the theory beyond residually finite groups. This includes recent and ongoing joint projects with Gardella, Hajac, Hirshberg, Hamblin, Tobolski and Zacharias.

Sep 13

Colloquium- Piotr M. Hajac (IMPAN) COLLOQUIUM HAS BEEN RESCHEDULED TO MONDAY 9/17/18, 4PM ROOM 150 MATH BLDG!!!

Thursday, September 13, 2018,

DUE TO SCHEDULING CONFLICTS THIS COLLOQUIUM WILL TAKE PLACE ON MONDAY, SEPTEMBER 17, 2018 @ 4PM IN ROOM 150 MATH BLDG.

Sep 14

G&T Seminar
Camille Horbez (CNRS/Fields Institute)
Growth under automorphisms of hyperbolic groups
4:00PM, Fri Sep 14 2018, 122 Math

Let G be a finitely generated group, let S be a finite generating set of G, and let f be an automorphism of G. A natural question is the following: what are the possible asymptotic behaviors for the length of f^n(g), written as a word in the generating set S, as n goes to infinity, and as g varies in the group G?
We investigate this question in the case where G is a torsion-free Gromov hyperbolic group. Growth was completely described by Thurston when G is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel’s work on train-tracks when G is a free group. We address the case of a general torsion-free hyperbolic group. We show in particular that every element g has a well-defined exponential growth rate under iteration of f, and that only finitely many exponential growth rates arise as g varies in G.
This is a joint work with Rémi Coulon, Arnaud Hilion and Gilbert Levitt.

Sep 17

Colloquium- Piotr M. Hajac (IMPAN) PLEASE NOTE RESCHEDULED FROM 9/13
OPERATOR ALGEBRAS THAT ONE CAN SEE
4:00PM, Mon Sep 17 2018, 150 Math Bldg.

Operator algebras are the language of quantum mechanics just as differential geometry is the language of general relativity. Reconciling these two fundamental theories of physics is one of the biggest scientific dreams. It is a driving force behind efforts to geometrize operator algebras and to quantize differential geometry. Among outcomes of these endeavors is noncommutatvive geometry, whose starting point is natural equivalence between commutative operator algebras (C*-algebras) and locally compact Hausdorff spaces. Thus noncommutative C*-algebras are thought of as quantum topological spaces, and researched from this perspective. However, such C*-algebras can enjoy features impossible for commutative C*-algebras, forcing one to abandon the algebraic-topology based intuition. Nevertheless, there is a class of operator algebras for which one can develop new ("quantum") intuition. These are graph algebras, C*-algebras determined by oriented graphs (quivers). Due to their tangible hands-on nature, graphs are extremely efficient in unraveling the structure and K-theory of graph algebras. We will exemplify this phenomenon by showing a CW-complex structure of the Vaksman-Soibelman quantum complex projective spaces.

Sep 18

Applied Math Seminar
Kenny Joseph (UB Computer Science) https://kennyjoseph.github.io/
Bayesian models of stereotyping and social categorization
3:50PM, Tue Sep 18 2018, 150 Math Bldg

Identities are the labels we use to categorize ourselves and others. Examples of identities include social roles, like ``doctor’’ and ``mother,’’ and group memberships, like ``Democrat’’ or ``Yankees fan’’. It is generally accepted that the ways we label (or categorize) ourselves and others with identities, and the ways others label us both impact our behavior. However, our ability to predict these labeling decisions, and the ensuing social behaviors that depend on them, is still largely limited to qualitative models of social cognition. I will present a string of recent efforts on formalizing the ways in which we stereotype and then categorize others, and how those categorizations then lead to social behaviors. I will also detail how I have leveraged these formalizations in empirical work on both social media and survey data.

Sep 18

Graduate Mentoring Seminar- Dr. William Menasco

5:00PM, Tue Sep 18 2018, Math 250

"Document your achievements."

Sep 19

Analysis Seminar
Yi Wang, UB​
Asymptotic stable division property and the Arveson-Douglas Conjecture.
4:00PM, Wed Sep 19 2018, 150 Math Bldg.

The Arveson-Douglas Conjecture concerns essential normality of submodules of the Bergman module. We will define the asymptotic stable division property and show that with additional mild conditions, the asymptotic stable division property implies essential normality. We will also apply this result on certain submodules. This gives us a unified proof of most known results on the Arveson-Douglas Conjecture. The proof is based on an inequality of a new type, a covering lemma and some local analysis.

Sep 20

Special Interdisciplinary Seminar- Ludwik Dabrowski (SISSA, Trieste)
"Almost commutative geometry of the Standard Model"
3:00PM, Thu Sep 20 2018, 150 Math Bldg.

A non-commutative C*-algebra is usually thought
of as the algebra of continuous functions on a "quantum space".
A. Connes encodes also smooth and metric structures
in terms of a certain analogue of the Dirac operator.
I will recall two natural Dirac-type operators on usual manifolds,
and present their analogues for the "almost commutative" algebra
that describes the Standard Model of fundamental particles in physics.

Sep 26

Analysis Seminar- Benjamin Hayes, University of Virginia
Local weak* convergence and the entropy of algebraic actions
4:00PM, Wed Sep 26 2018, 150 Math Bldg.

I will discuss the entropy of probability measure-preserving actions of sofic groups, due to Bowen and Kerr-Li. I will focus on the case when the action is by automorphisms of a compact metrizable group (these are called algebraic actions). I will give an abstract criterion, in terms of measures on model spaces, which guarantees that the measure-theoretic entropy and topological entropy agree. Knowledge of sofic groups and sofic entropy will not be assumed.

Oct 1

Algebra Seminar- Changlong Zhong, University at Albany
On the K-theoretic stable basis of Springer resolutions
4:00PM, Mon Oct 1 2018, 150 Mathematics Bldg.

Stable bases for various cohomology theories (singular cohomology, K-theory, and elliptic cohomology) were defined by Maulik and Okounkov. They are closely related with Hecke algebras. By using the twisted group algebra of Kostant and Kumar, I will give an algebraic definition of K-theoretic stable bases. Then I will talk about the formal root polynomial method, which is used to compute the restriction formula of stable bases. This is joint work with Changjian Su and Gufang Zhao.

Oct 2

Applied Math Seminar- John Medaglia, Drexel University
The Foundations and Frontiers of Cognitive Neuroengineering
3:50PM, Tue Oct 2 2018, 150 Math Bldg.

Cognitive neuroengineering is the intersection of cognitive neuroscience and neuroengineering. In cognitive neuroscience, we use many methods to measure real-time cognitive and neural activity. In neural engineering, we can stimulate and monitor changes in neurophysiological and cognitive activity in real-time contexts. In tandem, time-efficient algorithms are available to rapidly model input-output associations between brain stimulation, neural activity and measured behavior. Given these technologies, we can use conventional and emerging approaches from control engineering – a branch of systems engineering – to address pervasive problems in neuromodulation in experimental and clinical contexts. We can draw from cognitive neuroscience, engineering, and network science to confront these challenges.

Oct 5

G&T Seminar
Kiyoshi Igusa (Brandeis)
Equivariant Hatcher construction
4:00PM, Fri Oct 5 2018, 122 Math

This is a joint project with Tom Goodwillie extending earlier joint work with Goodwillie and Ohrt. The purpose of this project is to construct all exotic smooth structures on all smooth manifold bundles with a fiberwise group action in a stable range of dimensions. I will start by defining and enumerating the exotic smooth structures. By ``enumerate'' I mean compute the dimension of the vector space of exotic structures. To do this, we use a simplified version of Mackey functors.
We give a simple construction of these exotic structures using the irreducible real representations of a finite group G. We call it the ``equivariant Hatcher construction'' since it generalizes a classical construction due to Hatcher. We use higher Reidemeister torsion with coefficients in a Mackey functor to demonstrate that our construction (with all possible inputs) spans the vector space of all stable exotic structures on a fixed G-bundle.

Oct 8

Algebra Seminar
Debashish Goswami Indian Statistical Institute
(No) quantum symmetry for compact connected smooth manifolds
4:00PM, Mon Oct 8 2018, 150 Mathematics Bldg.

I 'll sketch the proof of the following theorem: there is no genuine
(not of the form C(G) for a compact group) compact quantum group which
can act faithfully and smoothly on C(M), where M is a compact
connected smooth manifold. The proof makes somewhat unexpected use of
some classical probabilistic techniques, besides the usual tools from
operator algebra and differential geometry.

Oct 12

G&T Seminar
Mahan Mj (Tata Institute/Fields Institute)
Bowen-Margulis measures and Extremal Cocycle Growth
4:00PM, Fri Oct 12 2018, Math 122

We establish a connection between extreme values of stable random fields arising in probability and groups G acting geometrically on CAT(-1) spaces X. The connection is mediated by the action of the group on its limit set equipped with the Patterson-Sullivan measure. Based on motivation from extreme value theory, we introduce an invariant of the action called extremal cocycle growth and show that its non-vanishing is equivalent to finiteness of the Bowen-Margulis measure for the associated unit tangent bundle U(X/G) provided X is not a tree whose edges are (up to scale) integers. We also establish an analogous statement for normal subgroups of free groups. This is joint work with Parthanil Roy.

Oct 15

Algebra Seminar- Gus Schrader, Columbia University
Dehn twists and Whittaker functions
4:00PM, Mon Oct 15 2018, 150 Mathematics Bldg.

The quantum higher Teichmuller theory developed by Fock and Goncharov
associates to a hyperbolic marked surface S and a simple Lie group G
an infinite dimensional unitary representation of the mapping class
group of S. In this talk, I'll describe the solution of the spectral
problem for the operators representing Dehn twists in quantum higher
Teichmuller theory for G=SL(n) and explain how the Dehn twist
eigenfunctions are given by with Whittaker functions for (the modular
double of) the quantum group U_q(sl(n)).

Joint work with Alexander Shapiro.

Oct 16

Applied Math Seminar- James Chen, UB Mechanical and Aerospace Engineering)
A Kinetic Description for Morphing Continuum
3:50PM, Tue Oct 16 2018, Math 150

The coupling between the intrinsic angular momentum and the hydrodynamic linear momentum has been known to be prominent in fluid flows involving physics across multiple length and time scales, e.g. turbulence, nonequilibrium flows and flows at micro-/nano-scale. Since the classical Navier-Stokes equations and Boltzmann’s kinetic theory are derived on the basis of monatomic gases or volumeless points, efforts to derive constitutive equations involving intrinsic rotation for fluids of polyatomic molecules have been found since the 1960s. One of the proposed continuum theories for polyatomic molecules was Morphing Continuum Theory (MCT). The theory was originally formulated under the framework of rational continuum mechanics and thermodynamic irreversible processes. The mathematically rigorous continuum mechanics presents a complete and closed set of governing equations, but leaves the physical meanings unexplained. Similar to the correlation between Boltzmann's kinetic theory and the classical continuum mechanics, an advanced kinetic theory involving the Boltzmann-Curtiss (B-C) distribution function and the B-C equation will be introduced for a morphing continuum. The method of the most probable distribution method is used to derive the Boltzmann-Curtiss distribution. The corresponding Boltzmann-Curtiss equations will be demonstrated to be the MCT governing equations without any dissipation terms, i.e. the system (flows with inner structures) is in equilibrium and at the Boltzmann-Curtiss distribution. A first-order approximation to the B-C distribution will be used to further derive the B-C transport equations. The corresponding governing equations will then be compared with the MCT equations. Furthermore, a path to reduce the presented MCT equations down to the classical N-S equations will be demonstrated and discussed.

Oct 19

G&T Seminar
Jing Tao (University of Oklahoma/Fields Institute)
Big Torelli groups
4:00PM, Fri Oct 19 2018, 122 Math

A surface S is of finite-type if its fundamental group is finitely generated; otherwise, it is of infinite type. The mapping class group MCG(S) of S is the group of isotopy classes of orientation-preserving homeomorphisms of S. This is a well-studied group when S has finite type, but big mapping class groups, i.e. MCG(S) of infinite-type surfaces, remain quite mysterious. But big mapping class groups arise naturally in various areas of mathematics and recently there has been a surge of interests in studying them. In this talk, I will discuss some recent results about the Torelli subgroup of MCG(S). This is joint with Aramayona, Ghaswala, Kent, McLeay, and Winarski.

Oct 30

Applied Math Seminar- Austin Benson, Cornell University
Simplicial closure and simplicial diffusions
3:50PM, Tue Oct 30 2018, Math 150

Networks are a fundamental abstraction of complex systems throughout the sciences and are typically represented by a graph consisting of nodes and edges. However, many systems have important higher-order interactions, where groups of nodes interact simultaneously, and such higher-order relations are not captured by a graph containing only pairwise connections. In the first part of the talk, we will explore the rich variety of higher-order interaction structure in empirical datasets and evaluate how well we can predict the appearance of new higher-order interactions, or what we call simplicial closure events. In the second part of the talk, we develop a model of diffusion for these higher-order interaction datasets. The key idea is to generalize the well-known relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian, the analog of the graph Laplacian for simplicial complexes. We can then use combinatorial Hodge theory to decompose the diffusions into components that reveal different types of structure. Throughout the talk, we will examine several real-world datasets, which come from social, biomedical, communication, human mobility, and commerce systems.

Oct 30

Graduate Mentoring Seminar- Dr. Adam Sikora

5:00PM, Tue Oct 30 2018, Math 250

"Math on the web and math computing".

Oct 31

Analysis Seminar- Alexandru Chirvasitu, SUNY at Buffalo
Incompressibility of compact groups
4:00PM, Wed Oct 31 2018, 150 Math Bldg.

The join X*Y of two topological spaces X and Y is the set of formal convex combinations of points from the two spaces. The join is a familiar construction to topologists, and arises naturally in the construction of the universal principal bundle for a topological group.

I will call a group G `incompressible' if there are no G-equivariant maps from higher to lower joins of copies of G. The main result is that all compact groups are incompressible, generalizing unpublished work by M. Bestvina and R. Edwards in the case of 0-dimensional groups.

Applications include a Borsuk-Ulam-type theorem for actions whose induced principal bundle is locally trivial.

(joint w/ Ludwik Dabrowski and Mariusz Tobolski)

Nov 5

Algebra Seminar-Vasu Tewari, University of Pennsylvania
Divided symmetrization and generalized permutahedra
4:00PM, Mon Nov 5 2018, 150 Mathematics Bldg

Generalized permutahedra are an important class of polytopes which
show up in many areas in mathematics. The volume and number of lattice
points of these polytopes are given by certain multivariate
polynomials that were introduced and +studied by Alex Postnikov, who
further established various remarkable combinatorial properties
thereof. In this talk, I will discuss in depth the procedure of
divided symmetrization that allows one to compute volumes of
generalized +permutahedra. Along the way, we will encounter familiar
combinatorial objects such as standard Young tableaux, reduced pipe
dreams, P-partitions and various Catalan objects.

This is joint work with Philippe Nadeau

Nov 6

Applied Math Seminar- Francois Meyer, University of Colorado, Boulder
Tracking the Evolution of Dynamic Networks
3:50PM, Tue Nov 6 2018, Math 150

To quantify the evolution of dynamic networks, one needs a notion of temporal difference that captures significant structural changes between two successive instants. We describe existing distances between graphs, and study their ability to reveal organizational changes. We propose a novel distance that can detect changes occurring on a graph at multiple scales. We develop a fast randomized algorithm to compute an approximation to this novel graph distance. We apply this novel distance to the analysis of a dynamic community graph. We detect the time at which the graph dynamics switches from a normal evolution -- where balanced communities grow at the same rate -- to an abnormal behavior -- where communities start merging. This is work in collaboration with Dr. Nathan Monnig, and Dr. Peter Wills.

Nov 6

Graduate Mentoring Seminar- Mr. Fred Stoss, Librarian, Lockwood Library

5:00PM, Tue Nov 6 2018, Math 250

“Finding Math in the UB Libraries: It’s Easy to Figure This!”

Nov 12

Algebra Seminar- Naihuan Jing, North Carolina State University
Presentation of Yangian algebras in BCD types.
4:00PM, Mon Nov 12 2018, 150 Mathematics Bldg

It is well-known that the R-matrix presentation of the Yangian in type A yields generators of
its Drinfeld presentation. It has been an open problem since Drinfeld's pioneering work
to extend this result to the remaining types.
We will provide a solution for the classical types of BCD
by constructing an explicit isomorphism between
the R-matrix and Drinfeld presentations of the Yangian.
It is based on an embedding theorem which allows us to consider
the Yangian of rank n-1 as a subalgebra of the Yangian of rank n of the same type.
This is joint work with A. Molev and M. Liu.

Nov 13

Applied Math Seminar- Hiroki Sayama, SUNY Binghamton
Graph product multilayer networks: spectral properties and applications
3:50PM, Tue Nov 13 2018, Math 150

This talk will introduce theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and strong product operators are considered, and then generalized. We first describe mathematical relationships between GPMNs and their factor networks regarding their degree/strength, adjacency, and Laplacian spectra, and then show that those relationships can still hold for non-simple and generalized GPMNs. We will also discuss applications of GPMNs in four areas: predicting epidemic thresholds, modelling propagation in non-trivial space and time, analysing higher-order properties of self-similar networks, and formulating evolutionary dynamics of organism-environment couplings.

Nov 15

Colloquium- Dr. Brian Hassard
Grading from scanned exams with mark-recognition recorded scores:
4:00PM, Thu Nov 15 2018, Math 250

This talk will discuss scanning and grading exams, as implemented in two
courses Fall 2018.

- the grader works on pdfs, one per problem, and records scores by
marking on a "scoring bar" at the bottom of each page

- in each reassembled exam, images of all scoring bars are copied to the
front page

- a pdf of all front pages (now containing scoring bar images) is written

- mark-recognition converts scoring bar images to numeric scores and a
file with scores for the class is written

- the instructor edits the file of scores while viewing the front page
images to check and possibly correct the scoring

- based on the edited file of scores, versions of the student exams are
created with summary tables of scores stamped on the front pages next to the
scoring bar images and with problem scores stamped on the individual problem pages

Issues encountered and the amount of time involved in each step will be discussed.

Nov 16

G&T Seminar
Bülent Tosun (Alabama)
Contact surgeries, symplectic fillings and Lagrangian discs
4:00PM, Fri Nov 16 2018, 122 Math

It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. In this talk, we will discuss some new results about positive contact surgeries and in particular completely characterize when contact (r)- surgery is symplectically/Stein fillable for r∈(0,1]. This is joint work with James Conway and John Etnyre.

Nov 30

G&T Seminar
Jacob Russell (CUNY)
Convexity in Hierarchically Hyperbolic Spaces
4:00PM, Fri Nov 30 2018, 122 Math

Convexity is a fundamental notion across a variety of flavors of geometry. In the study of the course geometry of metric spaces, it is natural to study quasiconvexity i.e. convexity with respect to quasi-geodesics. We study quasiconvexity in the class of hierarchically hyperbolic spaces; a generalization of Gromov hyperbolic spaces which contains the mapping class group, right-angled Artin and Coxeter groups, and many 3-manifold groups. ​ Inspired by the rich theory of quasiconvexity in hyperbolic spaces, we show that quasiconvex subsets of hierarchcially hyperbolic spaces mimic the behavior of quasiconvex subsets in hyperbolic spaces.