Hasan Saad- University of Virginia

In the 1960’s, Birch proved that the traces of Frobenius for elliptic curves taken at random over a large finite field is modeled by the semicircular distribution (i.e. the usual Sato-Tate for non-CM elliptic curves).  In analogy with Birch’s result, a recent paper by Ono, the author, and Saikia proved that the limiting distribution of the normalized Frobenius traces of a certain family of K3 surfaces 19 is the O(3) distribution. This distribution is quite different from the semicircular distribution. It is supported on [-3,3] and has vertical asymptotes at t=1 and t=-1. Here we make this result explicit by bounding the error term.

As a consequence, we are able to determine when a finite field is large enough for the discrete histograms to reach any given height near t=1. To obtain these results, we make use of the theory of Rankin-Cohen brackets in the theory of harmonic Maass forms.

Sam Shepherd – Vanderbilt

Bei Hu -University of Notre Dame- Math Colloquium to request Zoom Meeting ID and passcode.

Atherosclerosis is a leading cause of death worldwide; it originates from a plaque which builds up in
the artery. We considered a simplified model of plaque growth involving LDL and HDL cholesterols,
macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interfacebetween the plaque and the blood flow. In an earlier work (with Avner Friedman and Wenrui Hao) of an extremely simplified model, we proved that there exist small radially symmetric stationary plaques andestablished a sharp condition that ensures their stability. In our recent work (with Evelyn Zhao), we look for theexistence of non-radially symmetric stationary solutions. The absent of an explicit radially symmetric stationary solution presents a big challenge to verify the Crandall-Rabinowitz theorem; through asymptotic expansion, weextend the analysis to establish a finite branch of symmetry-breaking stationary solutions which bifurcate fromthe radially symmetric solutions. Since plaque is unlikely to be strictly radially symmetric, our result would beuseful to explain the asymmetric shapes of plaque. Our recent work (with Yaodan Huang, Xiaohong Zha) extends to other possible shapes as well as more realistic modeling efforts.

Host: Glenn Webb (glenn.f.webb@vanderbilt.edu), Xinyue Zhao (xinyue.zhao@vanderbilt.edu)ng,Zhengce Zhang)

Dongxiao Yu, University of Bonn.- Zoom link: https://vanderbilt.zoom.us/j/97526207493

In this talk, I will present a method to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. Starting from a global solution to the geometric reduced system satisfying several pointwise estimates, we find a matching exact global solution to the original quasilinear wave equations. As an application of this method, we will construct nontrivial global solutions to Fritz John’s counterexample ☐u=u_tu_{tt} and the 3D compressible Euler equations without vorticity for

Vladimir Shpilrain (CUNY)

Vladimir Shpilrain -CUNY- Math Colloquium to request Zoom Meeting ID and passcode.

Yao’s millionaires’ problem is: Alice has a private number a and Bob has a private number b, and the
goal of the two parties is to figure out which number is larger without revealing any information about a or b. We will discuss relations between this fun problem and serious problems like the possibility of secure public-key encryption and the P=NP? problem.

Host: A. Olshanskii (alexander.olshanskiy@vanderbilt.edu)

 Ian Tice, Carnegie Mellon University.

David Kribs- University of Guelph

Abstract- TBD

Alex Margolis -Vanderbilt

Abstract- TBA

Christopher Bishop -Stony Brook University

Weil-Petersson curves are a class of rectifiable closed curves in the plane, defined as the closure of the smooth curves with respect to the Weil-Petersson metric defined by Takhtajan and Teo in 2009. Their work solved a problem from string theory by making the space of closed loops into a Hilbert manifold, but the sameclass of curves also arises naturally in complex analysis, geometric measure theory, probability theory, knottheory, computer vision, and other areas. No geometric description of Weil-Petersson curves was known until2019, but there are now more than twenty equivalent conditions. One involves inscribed polygons and can beexplained to a calculus student. Another is a strengthening of Peter Jones’s traveling salesman conditioncharacterizing rectifiable curves. A third says a curve is Weil-Petersson iff it bounds a minimal surface inhyperbolic 3-space that has finite total curvature. I will discuss these and several other characterizations andsketch why they are all equivalent to each other. The lecture will contain many pictures, several definitions, but not too many proofs or technical details.

Host: Dechao Zheng (dechao.zheng@vanderbilt.edu)

Michael Davis- University of Iowa

Abstract- TBD

Ionut Chifan – University of Iowa

Abstract- TBA

Mehrdad Kalantar- University of Houston

Abstract- TBD

Jone Lopez de Gamiz Zearra -Vanderbilt

Sifan Yu, Vanderbilt University-PDE Seminar

Abstract: TBA.

Corey Jones, North Carolina State University

Asbtract- TBD

Elias Most, Princeton University

Dan Margalit – Georgia Tech

Dejan Gajic, Leipzig University- https://vanderbilt.zoom.us/j/992097409

Abstract- TBA

Peter Huston

Abstract- TBD

Ekaterina Rybak – Vanderbilt

https://my.vanderbilt.edu/mathbio/