
Date Time 
Location  Speaker 
Title – click for abstract 

02/16 4:00pm 
BLOC 302 
Julia Lindberg University of Texas 
On the typical and atypical solution to the Kuramoto equations
The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto equations as a system of algebraic equations, we first relate the complex root count of the Kuramoto equations to the combinatorics of the underlying network by showing that the complex root count is generically equal to the normalized volume of the corresponding adjacency polytope of the network. We then give explicit algebraic conditions under which this bound is strict and show that there are conditions where the Kuramoto equations have infinitely many equilibria. 

02/19 3:00pm 
BLOC 302 
Frank Sottile Texas A&M University 
Welschinger signs and the Wronski map
A general real rational plane curve C of degree d has 3(d2) flexes and (d1)(d2)/2 complex double points. Those double points lying in RP^2 are either nodes or solitary points. The Welschinger sign of C is (1)^s, where s is the number of solitary points. When all flexes of C are real, its parameterization comes from a point on the Grassmannian under the Wronskii map, and every parameterized curve with those flexes is real (this is the MukhinTarasovVarchenko Theorem). Thus to C we may associate the local degree of the Wronskii map, which is also 1 or 1. My talk will discuss work with Brazelton and McKean towards a possible conjecture that that these two signs associated to C agree, and the challenges to gathering evidence for this. 

02/26 4:00pm 
BLOC 302 
Stefano Marini University of Parma 
On finitely Levi nondegenerate closed homogeneous CR manifolds
A complex flag manifold F= G /Q decomposes into finitely many real orbits under the action of a real form of G. Their embedding into F define on them CR manifold structures. We give a complete classification of all closed simple homogeneous CR manifolds which have finitely nondegenerate Levi forms. 

03/08 4:00pm 
BLOC 302 
T. Mandziuk TAMU 
Border varieties of sums of powers
The variety of sums of r powers (VSP(F,r)) of a homogeneous degree d polynomial F is the closure in the Hilbert scheme of the set of all those rtuples of points of the dth Veronese variety that contain F in their linear span. As a main ingredient in their border apolarity theory, Buczyńska and Buczyński introduced the notion of a border variety of sums of powers. During the talk I will compare VSP(F,r) (and a similarly defined subset of the Hilbert scheme) with the border variety of sums of powers. The talk is based on a joint work with Emanuele Ventura. 

03/22 4:00pm 
BLOC 302 
Paulina Hoyos Restrepo UT Austin 
Manifold Learning in the Presence of Symmetries
Graph Laplacianbased algorithms for data lying on a manifold have proven effective for tasks such as dimensionality reduction, clustering, and denoising. Consider data sets whose data points lie on a manifold that is closed under the action of a known unitary matrix Lie group G. In this talk, I will show how to construct a Ginvariant graph Laplacian (GGL) by incorporating the distances between all the pairs of points generated by the action of G on the data set. The GGL converges to the LaplaceBeltrami operator on the data manifold, with a significantly improved convergence rate compared to the standard graph Laplacian, which uses only the distances between the points in the given data set. 

04/05 6:00pm 
TBA 

Texas Algebraic Geometry Symposium (TAGS)
see https://franksottile.github.io/conferences/TAGS24/index.html 

04/06 10:00am 
TBA 

Texas Algebraic Geometry Symposium (TAGS)
see https://franksottile.github.io/conferences/TAGS24/index.html 

04/12 4:00pm 
BLOC 302 
Brandon Ashley Southern Oregon University 
A GroupTheoretic Approach to Darboux Integrable $f$Gordon Equations
Classically, a partial differential equation is said to be Darboux integrable if its general solution can be found by only solving a system of ordinary differential equations. In this talk, we describe a transformation grouptheoretic approach to the study of Darboux integrable equations and highlight how this approach can be used to solve the equivalence problem for socalled $f$Gordon equations of the form $u_{xy} = f(x,y,u,u_x,u_y)$. 

04/15 3:00pm 
BLOC 302 
R. Ramkumar Cornell 
CartwrightSturmfels ideals and their moduli
CartwrightSturmfels ideals, CSideals for short, are multigraded ideals whose generic initial ideals are radical. First studied by Cartwright and Sturmfels, some examples include the ideals of maximal minors of a matrix of linear forms, binomial edge ideals, closure of linear spaces, and multiview ideals. In this talk, I will discuss the geometry of CSideals inside the multigraded Hilbert scheme, with a particular focus on bigraded CSideals. This is joint work with Alessio Sammartano. 

04/19 4:00pm 
BLOC 302 
Alex Cohen MIT 
An optimal inverse theorem for the rank of tensors
A polynomial f(x_1, … x_n) over a finite field has a large bias if its output distribution is far from uniform. It has rank `r' if we can write `f' as a function of polynomials g_1, …, g_r that each have smaller degree. Bias measures the amount of randomness, and rank measures the amount of structure. It is known that if `f' has small rank, it must have large bias. Green and Tao proved an inverse theorem stating that if `f' is significantly biased, its rank is bounded. Their bound was qualitative, however, and several authors gave quantitative improvements. We prove an optimal inverse theorem: the rank and the log of the bias are equivalent up to linear factors (over large enough fields). Our techniques are very different from the usual methods in this area, we rely on algebraic geometry rather than additive combinatorics. This is joint work with Guy Moshkovitz. 

04/26 4:00pm 
BLOC 302 
Karthik Ganapathy U. Michigan 
TBA 

04/29 3:00pm 
BLOC 302 
Akash Sengupta U. Waterloo 
TBA 

05/03 4:00pm 
BLOC 302 
Ronan Conlon UT Dallas 
A family of Kahler flying wing steady Ricci solitons
Steady KahlerRicci solitons are eternal solutions of the KahlerRicci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.D. Cao in complex dimension n>2. This is joint work with PakYeung Chan and Yi Lai. 

05/06 3:00pm 
BLOC 302 
F. Gesmundo U. Toulouse 
TBA 