Mathematics Department Colloquium
The Ohio State University
Year 20202021
Time: Thursdays 4:15 pm
Location: Virtual Zoom seminar

Schedule of talks:
Abstracts
(K. Falconer):
We will introduce selfsimilar 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 socalled runandtumble movements. This means that they alternate a jump (run phase) followed by fast reorganization phase (tumble) in which they decide of a new direction for run. For this reason, the population is described by a kineticBotlzmann 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 FluxLimitedKellerSegel system, in opposition to the traditional KellerSegel 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 kineticBoltzmann 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 2rig". Here we show that the category of Schur functors is the free symmetric 2rig 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. ZureickBrown):
TBD
(I. Coskun):
TBD
Past Ohio State University Mathematics Department Colloquia
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