Print Friendly printer friendly
 Events
Pontifical Catholic University of Chile (PUC)
Tue 24 Nov 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Online
Quantization of edge currents along magnetic interfaces: A K-theory approach
Online
Tue 24 Nov 2020, 3:30pm-4:30pm

Abstract

The purpose of this talk is to explain how to describe the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material using K-theory. We initially consider tight-binding magnetic models associated with generic magnetic multi-interfaces and we will describe the K-theoretical setting in which a bulk-interface duality can be derived. Then,  we will focus on  the (non trivial) case of the Iwatsuka magnetic field. The exposition is intended to be pedagogical and aimed at a non-specialist audience.
hide
University of Michigan–Ann Arbor
Tue 24 Nov 2020, 4:00pm
Discrete Math Seminar
https://ubc.zoom.us/j/62676242229?pwd=RURtUC9UYXEweVZTMTNGT1EvY1FLZz09
A generating function for counting mutually annihilating matrices over a finite field
https://ubc.zoom.us/j/62676242229?pwd=RURtUC9UYXEweVZTMTNGT1EvY1FLZz09
Tue 24 Nov 2020, 4:00pm-5:00pm

Abstract

In 1958, Fine and Herstein proved that the an n by n matrix over the finite field F_q has a probability of q^{-n} to be nilpotent. A clever application of this result can lead to the formula \sum_{H: abelian p-group} 1/|Aut(H)| = 1/((1-p^-1)(1-p^-2)...), which is fundamental in building the Cohen--Lenstra distribution of abelian p-groups. There are other matrix enumeration results, including the counting of pairs of commuting matrices (Feit and Fine) and the counting of pairs of commuting nilpotent matrices (Fulman), all presented as generating functions that can be expressed as infinite products of rational functions. I will explain why all these above are the special cases of one general problem related to a moduli space in algebraic geometry, and why the following is the next unknown case of the problem: count the number of pairs of n by n matrices (A,B) such that AB=BA=0 (hence the word "mutually annihilating" in the title). In my recent work, I gave a generating function that answers this question, and factorized it into the form 1/((1-x)(1-q^-1 x)(1-q^-2 x)...)^2 H(x), where H(x) is an entire holomorphic function given explicitly by an infinite sum. Interesting analytic properties of H(x) will be discussed. 
hide
Nina Miolane
UC Santa Barbara
Wed 25 Nov 2020, 11:00am
Mathematical Biology Seminar
Zoom - contact organizer (abuttens at math ubc ca) for meeting id
Geometric statistics for shape analysis of bioimaging data
Zoom - contact organizer (abuttens at math ubc ca) for meeting id
Wed 25 Nov 2020, 11:00am-12:00pm

Abstract

The advances in bioimaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, statistical analyses in biomedical research are poised to incorporate more shape data. This leads to the question: how do we define quantitative descriptions of shape variability from images? 

 

Mathematically, landmarks’ shapes, curve shapes, surface shapes, or shapes of objects in images are data that belong to non-Euclidean spaces, for example to Lie groups or quotient spaces. In this context, we introduce  “Geometric statistics”, a statistical theory on non-Euclidean spaces. We present several studies showing the theory and applications of Geometric Statistics to the analysis of biomedical shape data.


 

hide
University of British Columbia
Wed 25 Nov 2020, 2:00pm
Topology and related seminars
Zoom
Rational cuspidal curves, surfaces of Bogomolov-Miyaoka-Yau type, and rational homology cobordism: old and new problems at the crossroad of algebraic geometry and low dimensional topology.
Zoom
Wed 25 Nov 2020, 2:00pm-3:00pm

Abstract

A classical problem in algebraic geometry asks what rational cuspidal curves can be realised in the complex projective plane. In the last few years some substantial advancement regarding this problem have been made, also based on the methods of Heegaard Floer homology. I will discuss some open problems, conjectures, and constructions.  This is joint work with Paolo Aceto (Oxford University).

Note for Attendees

 https://ubc.zoom.us/j/63532469289?pwd=b0RJYi9oOHAxRTY1QW5BOEdnMUU5Zz09 
 
passcode: 46972
hide
Duke
Wed 25 Nov 2020, 3:00pm
Probability Seminar
https://ubc.zoom.us/j/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
The minimum modulus for random trigonometric polynomials
https://ubc.zoom.us/j/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
Wed 25 Nov 2020, 3:00pm-4:30pm

Abstract

We consider the restriction to the unit circle of random degree-n polynomials with iid normalized coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows a limiting exponential distribution. We show this is a universal phenomenon, extending their result to arbitrary sub-Gaussian coefficients, such as Rademacher signs. For discrete distributions we must now deal with possible arithmetic structure in the polynomial evaluated at different points of the circle. Our proof divides the circle into major arcs that are well approximated by rationals, which we handle by crude arguments, and complementary minor arcs, for which we obtain strong comparisons with the Gaussian model via sharp decay estimates on characteristic functions. Based on joint work with Hoi Nguyen.
hide
San Francisco State University
Fri 27 Nov 2020, 9:00am
Algebraic Geometry Seminar
https://ubc.zoom.us/j/67916711780(password:the number of lines on a generic quintic threefold)
Putting the "volume" back in volume polynomials
https://ubc.zoom.us/j/67916711780(password:the number of lines on a generic quintic threefold)
Fri 27 Nov 2020, 9:00am-10:30am

Abstract

It is a strange and wonderful fact that Chow rings of matroids behave in many ways similarly to Chow rings of smooth projective varieties. Because of this, the Chow ring of a matroid is determined by a homogeneous polynomial called its volume polynomial, whose coefficients record the degrees of all possible top products of divisors. The use of the word "volume" is motivated by the fact that the volume polynomial of a smooth projective toric variety actually measures the volumes of certain polytopes associated to the variety. In the matroid setting, on the other hand, no such polytopes exist, and the goal of our work was to find more general polyhedral objects whose volume is measured by the volume polynomial of matroids. In this talk, I will motivate and describe these polyhedral objects. This is joint work with Anastasia Nathanson.
hide
UBC Mathematics
Fri 27 Nov 2020, 3:00pm
Department Colloquium
zoom
Graduate Research Award: Bulk-surface coupled models: coupling passive diffusion in bounded domains to dynamically active boundaries
zoom
Fri 27 Nov 2020, 3:00pm-4:00pm

Abstract

Motivated by the spatial segregation of intracellular proteins between the cytoplasm and the cellular membrane, we investigate the spatio-temporal dynamics of bulk-surface coupled models. For such models, a passive diffusion process occurring inside a bounded domain is coupled to a nonlinear reaction-diffusion process restricted to the boundary. A variety of idealized bulk geometries are considered, that consist of 1-D intervals and 2-D circular domains. Our emphasis is on the analysis of bifurcations, which characterize the onset of qualitative changes in the overall dynamics resulting from parameters crossing through critical values. A combination of analytical and numerical methods are employed to determine the stability of bifurcating solutions.

hide
UCLA
Mon 30 Nov 2020, 8:00am
Algebraic Groups and Related Structures
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Degree One Milnor K-Invariants of Groups of Multiplicative Type
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Mon 30 Nov 2020, 8:00am-9:00am

Abstract

 Many important algebraic objects can be viewed as G-torsors over a field F, where G is an algebraic group over F. For example, there is a natural bijection between F-isomorphism classes of central simple F-algebras of degree n and PGLn(F)-torsors over Spec(F). Much as one may study principal bundles on a manifold via characteristic classes, one may likewise study G-torsors over a field via certain associated Galois cohomology classes. This principle is made precise by the notion of a cohomological invariant, which was first introduced by Serre. 

In this talk, we will determine the cohomological invariants for algebraic groups of multiplicative type with values in H1(-, Q/Z(1)). Our main technical analysis will center around a careful examination of mun-torsors over a smooth, connected, reductive algebraic group. Along the way, we will compute a related group of invariants for smooth, connected, reductive groups.  

hide
 
Top