Mathematics Department Colloquium 
The Ohio State University

  Year 2020-2021

Time: Thursdays 4:15 pm
Location: Virtual Zoom seminar

YouTube channel

Schedule of talks:


 

TIME  SPEAKER TITLE
August 27  
Th 4:15pm
Kenneth Falconer 
(University of St Andrews) 
Symmetry and Enumeration of Fractals
September 10  
Th 4:15pm
Michael Larsen 
(Indiana U) 
The Circle Method in Algebraic Geometry
September 17  
Th 4:15pm
Adrian Ioana 
(UCSD) 
Classification and rigidity for group von Neumann algebras
October 29  
Th 4:15pm
Benoit Perthame 
(Sorbonne-Université) 
Bacterial movement by run and tumble: models, patterns, pathways, scales
November 5  
Th 4:15pm
John Baez 
(UC Riverside) 
Schur Functors
November 12  
Th 4:15pm
Joel Kamnitzer 
(U Toronto) 
Categorification of representations and generalized affine Grassmannian slices
November 19  
Th 4:15pm
Lizhen Ji 
(U Michigan) 
Geometric Schottky Problem
December 3  
Th 4:15pm
Izabella Laba 
(UBC) 
TBD
January 14  
Th 4:15pm
David Zureick-Brown 
(Emory) 
TBD
January 21  
Th 4:15pm
Gunnar Carlsson 
(Stanford) 
TBD
February 4  
Th 4:15pm
Bianca Viray 
(U Washington) 
TBD
February 11  
Th 4:15pm
Izzet Coskun 
(UIC) 
TBD



Abstracts

(K. Falconer): We will introduce self-similar fractals and consider families of such fractals where the similarities are defined using certain templates. We will show how ideas from group theory can be used to enumerate the distinct fractals in these families and to classify their symmetries.

(M. Larsen): Certain counting problems in group theory can be formulated either in terms of varieties over finite fields, or (dually) in terms of irreducible character values. By comparing the two points of view, one can either use geometry to give character estimates or (what I will mostly talk about) character estimates to prove theorems in geometry.

(A. Ioana): Any countable group G gives rise to a von Neumann algebra L(G). The classification of these group von Neumann algebras is a central theme in operator algebras. I will survey recent rigidity results which provide instances when various algebraic properties of groups, such as the presence or absence of a direct product decomposition, are remembered by their von Neumann algebras.

(B. Perthame): At the individual scale, bacteria as E. coli move by performing so-called run-and-tumble movements. This means that they alternate a jump (run phase) followed by fast re-organization phase (tumble) in which they decide of a new direction for run. For this reason, the population is described by a kinetic-Botlzmann equation of scattering type. Nonlinearity occurs when one takes into account chemotaxis, the release by the individual cells of a chemical in the environment and response by the population. These models can explain experimental observations, fit precise measurements and sustain various scales. They also allow to derive, in the diffusion limit, macroscopic models (at the population scale), as the Flux-Limited-Keller-Segel system, in opposition to the traditional Keller-Segel system, this model can sustain robust traveling bands as observed in Adler's famous experiment. Furthermore, the modulation of the tumbles, can be understood using intracellular molecular pathways. Then, the kinetic-Boltzmann equation can be derived with a fast reaction scale. Long runs at the individual scale and abnormal diffusion at the population scale, can also be derived mathematically.

(J. Baez): The representation theory of the symmetric groups is clarified by thinking of all representations of all these groups as objects of a single category: the category of Schur functors. These play a universal role in representation theory, since Schur functors act on the category of representations of any group. We can understand this as an example of categorification. A "rig" is a "ring without negatives", and the free rig on one generator is N[x], the rig of polynomials with natural number coefficients. Categorifying the concept of commutative rig we obtain the concept of "symmetric 2-rig". Here we show that the category of Schur functors is the free symmetric 2-rig on one generator.

(J. Kamnitzer): The geometric Satake correspondence links representations of a semisimple group with the geometry of the affine Grassmannian. From this perspective, it is natural to try to categorify representations using quantizations of affine Grassmannian slices. Remarkably these affine Grassmannian slices also appear in physics as Coulomb branches of 3d supersymmetric gauge theories. This connection allows us to generalize affine Grassmannian slices and achieve the desired categorification.

(L. Ji): The notion of Riemann surfaces was introduced by Riemann in his thesis in 1851, and the moduli space M_g of compact Riemann surfaces of genus g was introduced by Riemann in his masterpiece on abelian functions in 1857. When g>1, M_g is not a locally symmetric space, but shares some intriguing similarities with it. The important Jacobian map embeds M_g into the Siegel modular variety A_g, a very important locally symmetric space. The classical Schottky problem is concerned with the characterization of the image of M_g in A_g as an algebraic subvariety. In this talk, we will discuss metric properties of the image with respect to the locally symmetric metric of A_g, for example, about the metric distortion and the large scale geometry.

(I. Laba): TBD


(B. Viray): TBD

(G. Carlsson): TBD

(D. Zureick-Brown): TBD

(I. Coskun): TBD


Past Ohio State University Mathematics Department Colloquia


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