Bogdan Chornomaz, Vanderbilt University
Location: Stevenson 1312

In this talk we will address the SSP ?= RC conjecture, which we were discussing last semester. SSP is a class of finite lattices satisfying Sauer-Shelah-Perles, that is, lattices in which every set of elements shatters at least as many elements as it has. The conjecture says that those are exactly finite relatively complemented lattices, and, while it is almost trivial to show that SSP implies RC, the opposite direction does not seem to be easy. We will briefly recall the basic properties of RC lattices and a sufficient condition for SSP. Then we present recent advancements towards the proof.

Location: Stevenson 1425

Rachel Skipper, The Ohio State University
Location: Stevenson 1308

A group is said to be of type $F_n$ if it admits a classifying space with compact $n$-skeleton. We will consider the class of R\”{o}ver-Nekrachevych groups, a class of groups built out of self-similar groups and Higman-Thompson groups, and use them to produce a simple group of type $F_{n-1}$ but not $F_n$ for each $n$. These are the first known examples for $n\geq 3$. As a consequence, we find the second known infinite family of quasi-isometry classes of finitely presented simple groups.

Ben Breen, Dartmouth College
Location: Stevenson 1320

We describe heuristics in the style of Cohen-Lenstra for narrow class groups and units in abelian extensions of odd degree. These results stem from a model for the 2-Selmer group of a number field. We conclude with computational evidence for cyclic extensions of degree n = 3,5,7.

Alexander Olevskii, Tel Aviv University
Location: Stevenson 5211

After a short introduction to Riemann’s uniqueness theory I will discuss the following problem, going back to early 60-s: Can a (non-trivial) trigonometric series
\sum c(n) e^inx ,    c( n) = o(1),
have a subsequence of partial sums which converges to zero everywhere? Joint work with Gady Kozma. Tea at 3:33 pm in SC 1425. (Host: Akram Aldroubi)

Lauren Gaydosh, Vanderbilt University
Location: Garland Hall 101

Jun Yang, Vanderbilt University
Location: Stevenson 1432

There is a family of algebras associated with the Motzkin numbers and a parameter d. We will prove that one can construct a hyperfinite $II_1$ factor from them if and only if d is $2cos(\pi/n)+1, (n\geq 3)$ or no less than 3. We will construct a sequence of bimodules over it. Then we will discuss the irreducibility, dimensions and get a fusion rule of $A_n$. This is joint work with Vaughan Jones.

Vu Hoang, The University of Texas at San Antonio
Location: Stevenson 1307

In classical electrodynamics, the self-force of a charged particle on itself is undefined, leading to a major inconsistency in the equations of motion for point particles. The usual solution of the problem involves a renormalization procedure, which is mathematically not well defined. It appears that a successful solution of this problem requires a modification of the Maxwell-Lorentz equations. In this talk, I consider the field equations of higher-order electrodynamics as proposed by Bopp, Lande, Thomas and Podolsky in the 1940’s. This theory modifies the Maxwell Lagrangian by adding terms containing higher-order derivatives of the field tensor, leading to higher-order wave equations that couple charged particles to their radiation fields. Starting with a brief review of the subject’s history, I will focus on recent results by Kiessling-Tahvildar-Zadeh and by M. Radosz and myself, showing that a covariant equation of motion for point particles can be rigorously derived from the postulate of conservation of energy and momentum without any renormalization. I will also present a global existence result for the motion of a single particle under the influence of an external field and its radiation reaction. This is joint work with M. Radosz.

Brian Luczak, Vanderbilt University
Location: Stevenson 1206

Ahram Feigenbaum, Vanderbilt University
Location: Stevenson 1313

The sphere packing problem asks for the densest collection of non-overlapping congruent spheres in $\mathbb{R}^n$. In 2016, Viazovska proved that the $E_8$ lattice is optimal for $n = 8$. Subsequently, she with Cohn, Kumar, Miller, and Radchenko that showed the Leech lattice was optimal for $n =24$. Their proofs relied on the theory of weakly holomorphic and quasi-modular forms to construct Fourier eigenfunctions with prescribed zeros at distances in the $E_8$ and Leech lattices. Similar ideas were applied by Radchenko and Viazovska to obtain interpolation formulas for real Schwartz functions and by Cohn and Gon\c{c}alves to study uncertainty principles in harmonic analysis. In this thesis, we develop a unified approach to the construction of such functions. We show that the weakly holomorphic and weakly quasi-modular forms behind them are uniquely defined by the conditions that they be eigenfunctions of the Fourier transform belonging to the Schwartz class. We construct the Fourier eigenfunctions for all $n$ divisible by 4. We also show an extension of the interpolation formula given by Radchenko and Viazovska in $\mathbb{R}$ to radial functions in $\mathbb{R}^2$ and $\mathbb{R}^3$.

Anton M. Zeitlin, Louisiana State University
Location: Stevenson 1432

The Teichmueller space parametrizes Riemann surfaces of fixed topological type and is fundamental in various contexts of mathematics and physics. It can be defined as a component of the moduli space of flat G=PSL(2,R) connections on the surface. Higher Teichmueller space extends these notions to appropriate higher rank classical Lie groups G, and N=1 super-Teichmueller space likewise studies the extension to the super Lie group G=OSp(1|2). In this talk, I will discuss the solution to the long-standing problem of giving Penner-type coordinates on super-Teichmueller space and its higher analogues and will also talk about several applications of this theory including the recent generalization of the McShane identity to the super case.

Location: Edwin Warner Park Picnic Shelter 11

Hayden Jananthan, Vanderbilt University
Location: Stevenson 1206

Glenn Webb, Vanderbilt University
Location: Stevenson 1206

Jean Pierre Mutanguha, University of Arkansas
Location: Stevenson 1308

Ayla Gafni, University of Mississippi
Location: Stevenson 1320

Mihaela Ifrim, University of Wisconsin Madison
Location: Stevenson 1307

Andy Jarnevic, Vanderbilt University
Location: Stevenson 1206

Daniel Studenmund, Notre Dame
Location: Stevenson 1308

Lauren Ruth and Alex Cameron, Vanderbilt University
Location: Stevenson 1206

Lauren Ruth, Vanderbilt University
Location: Stevenson 1308

Brent Nelson, Michigan State University
Location: Stevenson 1432

Zach Tripp, Vanderbilt University
Location: Stevenson 1206

Jason Behrstock, CUNY
Location: Stevenson 1308

Bin Gui, Rutgers University
Location: Stevenson 1432

Theodore Drivas, Princeton University
Location: Stevenson 1307

Genevieve Walsh, Tufts University
Location: Stevenson 1308

John Voight, Dartmouth College
Location: Stevenson 1320