MONDAY - 4/15/24
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Combinatorics Seminar
Location: 182 Goegre, Room 110 Time: 12:00-1:00pm Speaker: Raluca Vlad, Brown University Title: The Combinatorics of Graph Curves Abstract: A graph curve is an algebraic curve consisting of a union of lines with each line intersecting precisely three other lines in nodes. The dual graph of such a curve is therefore a simple trivalent graph. In my talk, I will discuss some properties of graph curves that are governed by the combinatorics of their dual graphs. In particular, I will describe how the matroid encoding the point configuration in a hyperplane section of a graph curve can be constructed from the dual graph. Moreover, I will explain how the dual graph governs the possible deformations (“smoothenings”) of a graph curve and use it to characterize when a graph curve can be deformed into a smooth maximal curve. This is based on joint work with A. Geiger, K. Kuehn, M. Kummer, S. Hashimoto, and B. Sturmfels. |
Analysis Seminar
Location: Kassar 105 Time: 3:00-4:00pm Speaker: Stefano Decio, IAS Title: Robin harmonic measure in rough domains Abstract: I will describe the construction of a harmonic measure that reproduces a harmonic function from its Robin boundary data, which is a combination of the value of the function and its normal derivative. I shall discuss the surprising fact that this measure turns out to be (quantitatively) mutually absolutely continuous with respect to surface measure on a wide class of domains that includes the complement of certain fractals. Based on joint work with Guy David, Max Engelstein, Svitlana Mayboroda and Marco Michetti. |
Number Theory & Algebra Seminar
Location: Kassar 105 Time: 4:00-5:00pm Speaker: Santiago Arango-Piñeros, Emory Title: Counting 5-isogenies of elliptic curves over the rationals. Abstract: We study the asymptotic order of growth of the number of 5-isogenies of elliptic curves over the rationals, with bounded naive height. This is forthcoming work in collaboration with Changho Han, Oana Padurariu, and Sun Woo Park. |
TUESDAY - 4/16/24
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Graduate Student Seminar
Location: Kassar 105 Time: 12:00-1:00pm Speaker: Sam Freedman, Brown University Title: What is…a mapping class group? (Reprise) Abstract: My very first grad seminar talk in fall 2018 was about mapping class groups. It was probably a bad talk (even if everyone was too polite to tell me that). For my last grad seminar talk, I will attempt to use what I’ve learned these past 6 years to give a talk on mapping class groups that is bad for different, more mature reasons. |
Geometric Analysis Seminar
Location: GEO155 106 (155 George Street, side entrance) Time: 3:00-4:00pm Speaker: Steve Gindi, Brandeis Title: Long time limits of Ricci flow Abstract: We derive rigidity results for Ricci flow blowdown limits on classes of nilpotent principal bundles. We accomplish this by constructing new functionals over the base manifold that are monotone along the flow. This will have applications to the long time behavior and the collapsing of Ricci flow solutions in all dimensions. |
Graduate Lecture Series in Analysis and PDEs (GLESPA)
Location: Kassar 105 Time: 4:00-5:30pm Speaker: Wenrui Huang, Brown University Title: Stationary Phase and Dispersive Estimates Abstract: Dispersive estimates are crucial to studying nonlinear dispersive PDEs. One standard method for obtaining dispersive estimates is the stationary phase method. In these lectures, I will discuss the stationary phase lemma from 1D (Van Der Corput Lemma) to higher dimensions. Then, I will apply the lemma to prove dispersive estimates for many PDEs, such as the Schrodinger, KdV, wave, and Klein-Gordon Equations. |
WEDNESDAY - 4/17/24
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Geometry & Topology Seminar
Location: Kassar 105 Time: 3:00-4:00pm Speaker: Kasra Rafi, Toronto Title: Benjamini-Schramm limits of high genus translation surfaces Abstract: A sequence of random finite-volume manifolds X_i Benjamini-Schramm converges to a random pointed manifold (X,p) if, when p_i is a random point in X_i chosen uniformly, then the law of (X_i, p_i) converges to the law of (X, p) in the space of Borel probability measures on the space of pointed manifolds. This convergence notion admits natural generalizations to manifolds endowed with extra structures, such as abelian differentials. We will describe the Benjamini-Schramm limit of a random translation surface of genus g as g approaches infinity. This is a joint work in progress with Lewis Bowen and Hunter Vallejos. |
FRIDAY - 4/19/24
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Algebraic Geometry Seminar
Location: Kassar 105 Time: 3:00-4:00pm Speaker: Karl Christ, University of Texas, Austin Title: Irreducibility of Severi varieties on toric surfaces
Abstract: Severi varieties parametrize integral curves of fixed |
PDE Seminar
Location: 170 Hope Street, Room 108 Time: 3:00-4:00pm Speaker: Gerard Castro-López, Brown University Title: Existence of non convex V-states Abstract: V-states are uniformly rotating vortex patches of the 2D Euler equation. The only known explicit examples are circles and ellipses, the rest of positive existence results use local or global bifurcation arguments and don’t give any quantitative information of the solutions. I will talk about the existence of solutions far from the perturbative regime, being able to extract nontrivial features of them and a precise quantitative description. We will use a combination of analysis and computer assisted proofs techniques. This is joint work with Javier Gómez-Serrano. |
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