## Seminars and Colloquia Schedule

### On the length of the shortest closed geodesic on positively curved 2-spheres.

Series
Geometry Topology Seminar
Time
Monday, April 26, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/579155918
Speaker
Franco Vargas PalleteYale University

Following the approach of Nabutovsky and Rotman for the curve-shortening flow on geodesic nets, we'll show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. On the pinched curvature setting, we prove a bound on the first eigenvalue of the Laplacian and use it to prove a new isoperimetric inequality for pinched 2-spheres sufficiently close to being round. This allows us to improve our bound on the length of the shortest closed geodesic in the pinched curvature setting. This is joint work with Ian Adelstein.

### Some problems in point-set registration

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 26, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/884917410
Speaker
Yuehaw KhooUniversity of Chicago

In this talk, we discuss variants of the rigid registration problem, i.e aligning objects via rigid transformation. In the simplest scenario of point-set registration where the correspondence between points are known, we investigate the robustness of registration to outliers. We also study a convex programming formulation of point-set registration with exact recovery, in the situation where both the correspondence and alignment are unknown. This talk is based on joint works with Ankur Kapoor, Cindy Orozco, and Lexing Ying.

### Maximum number of almost similar triangles in the plane

Series
Graph Theory Seminar
Time
Tuesday, April 27, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Bernard LidickýIowa State University

A triangle $T'$ is $\varepsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\varepsilon$. Given a triangle $T$, $\varepsilon >0$ and $n \in \mathbb{N}$, Bárány and Füredi asked to determine the maximum number of triangles $h(n,T,\varepsilon)$ being $\varepsilon$-similar to $T$ in a planar point set of size $n$. We show that for almost all triangles $T$ there exists $\varepsilon=\varepsilon(T)>0$ such that $h(n,T,\varepsilon)=n^3/24 (1+o(1))$. Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof. This is joint work with József Balogh and Felix Christian Clemen.

### Macdonald and Schubert polynomials from Markov chains

Series
School of Mathematics Colloquium
Time
Thursday, April 29, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Lauren K. WilliamsHarvard University

Two of the most famous families of polynomials in combinatorics are Macdonald polynomials and Schubert polynomials. Macdonald polynomials are a family of orthogonal symmetric polynomials which generalize Schur and Hall-Littlewood polynomials and are connected to the Hilbert scheme.  Schubert polynomials also generalize Schur polynomials, and represent cohomology classes of Schubert varieties in the flag variety. Meanwhile, the asymmetric exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, which was initially introduced by Macdonald-Gibbs-Pipkin to provide a model for translation in protein synthesis.  In my talk I will explain how two different variants of the ASEP have stationary distributions which are closely connected to Macdonald polynomials and Schubert polynomials, respectively.  This leads to new formulas and new conjectures.

This talk is based on joint work with Corteel-Mandelshtam, and joint work with Donghyun Kim.

### Steady waves in flows over periodic bottoms

Series
CDSNS Colloquium
Time
Friday, April 30, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Carlos Garcia AzpeitiaUNAM

In this talk we present the formation of steady waves in two-dimensional fluids under a current with mean velocity $c$ flowing over a periodic bottom. Using a formulation based on the Dirichlet-Neumann operator, we establish the unique continuation of a steady solution from the trivial solution for a flat bottom, with the exception of a sequence of velocities $c_{k}$.  Furthermore, we prove that at least two steady solutions for a near-flat bottom persist close to a non-degenerate $S^1$-orbit of steady waves for a flat bottom. As a consequence, we obtain the persistence of at least two steady waves close to a non-degenerate $S^1$-orbit of Stokes waves bifurcating from the velocities $c_{k}$ for a flat bottom. This is a joint work with W. Craig.

### Global Constraints within the Developmental Program of the Drosophila Wing

Series
Mathematical Biology Seminar
Time
Friday, April 30, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker