Johns Hopkins UniversityEST. 1876
America’s First Research University
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09:10 Siddharth Mahendraker (Boston College): Towards the stabilization of the relative trace formula for the Galois period on SL(2).09:55 Coffee break.10:15Zhaolin Li (Minnesota): Fundamental lemma for rank one spherical varieties.11:10Connor Halleck-Dubé (Berkeley): ξ-stability and the Weighted Fundamental Lemma.12:00 Lunch break.13:30Dongryul Kim (Stanford): Igusa stacks and the p-adic geometry of Shimura varieties.14:25Hao Peng (MIT): An R=T theorem […] |
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Title: Geometric engineering in Topological Modular FormsAbstract: “Geometric engineering” is a terminology in physics, referring to processes creating interesting QFTs out of simple pieces, by sequence of basic geometric processes. I will explain my ongoing project to mimic that in elliptic cohomology theory, guided by Segal-Stolz-Teichner paradigm. I will explain the progress on the cases […]
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Title: Compensation phenomena for concentration effects via nonlinear elliptic estimatesAbstract: We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates for the lack of ellipticity of the differential […] |
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Title: Crepant resolutions of log-terminal singularities via Artin stacks (following Satriano--Usatine) |
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Title: The Irregular Elliptic Stark Conjecture Abstract: In a joint work with Victor Rotger, we study the irregular elliptic Stark conjecture of Darmon, Rotger, and Lauder. The fixed data consists of a rational elliptic curve $E_f$ and 2-dimensional artin representations $rho_g,rho_h : text{Gal}(H/{mathbb{Q}}) rightarrow GL_2(L)$ such that the selmer group $text{Hom}_{G_{mathbb{Q}}}(rho_g otimes rho_h , E(H))$ […] |
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Title: Monotone sweepouts and minimal surfaces Abstract: In this talk, I will discuss the notion of monotone homotopies and sweepouts - what they are, when they exist, and why we care about them. In particular, we will show how they are related to the existence of minimal surfaces in certain noncompact settings, as well as recent […] |
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Title: Compact components of character varietiesAbstract: Relative character varieties of surface groups are varieties which parametrize representations of the fundamental group of a surface with prescribed behavior the punctures of the surface. In the 90s, Benedetto and Goldman discovered a surprising compact component of a (real) relative character variety, later generalized by the work of Deroin-Tholozan and […]
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Title: Knot complements, series invariants and Lie superalgebra Abstract: Inspired by the categorification program for a numerical invariant of three-manifolds at roots of unity, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized […] |
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Title: On the Bloch–Kato Conjecture for some four-dimensional symplectic Galois representations Abstract: The Bloch–Kato Conjecture predicts a relation between Selmer ranks and orders of vanishing of L-functions for Galois representations arising from etale cohomology of algebraic varieties. In this talk, I’ll describe results towards this conjecture in ranks 0 and 1 for the self-dual Galois representations […] |
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Title: Z/2 harmonic 1-forms and harmonic maps to trees Abstract: The notion of a Z/2 harmonic 1-form (or spinor) was introduced by Taubes, who showed that they appear as limiting objects of the space of flat SL(2,C) connections on closed 3-manifolds. They similarly appear in other gauge theoretic situations that exhibit noncompact phenomena. Understanding their structure […] |
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Title: Intermittency and dissipation in fluid turbulenceAbstract: Intermittency is a remarkable and robust feature of three-dimensional turbulence for which we still lack explanation from first principles. It will be shown how a dissipation with a non-trivial lower-dimensional part induces a quantitative intermittent regularity on the weak solution. |
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Title: On the Yau--Tian--Donaldson conjecture for extremal metricsAbstract: Let X be a compact Kähler manifold. Calabi asked whether a given Kähler class on X contains a "canonical" Kähler metric, such as an extremal metric. Roughly speaking, the Yau-Tian-Donaldson conjecture states that if the Kähler class is the first Chern class of an ample line bundle, then the […]
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Title: Hecke algebras, KLR algebras, and James's conjectureAbstract: I will give a brief account of the combinatorial representation theory of type A Iwahori–Hecke algebras, and their realisation as cyclotomic KLR algebras. In this story, I will largely focus on the decomposition number problem as one of the key problems in this field, and James's conjecture, which […] |
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Title: Counting points without abelian varieties Abstract: Counting mod p points on Shimura varieties has been for a few decades the main avenue for establishing non-abelian reciprocity laws. This began with the work of Deligne and Langlands on the modular curve, continued with that of Kottwitz on PEL type Shimura varieties, and has culminated in recent […] |
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Title: Immersions of small normal curvature Abstract: Given a closed manifold and a sufficiently large integer N, we study the smallest possible normal curvature, C_N(X), of all immersions of X into the unit ball of the N dimensional Euclidean space. This question was recently initiated by Gromov, who studied the case when X is the […] |
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Title: On Putative Self-Similarity for Incompressible 3D EulerDescription: We study hypothetical finite-time self-similar blow-up solutions to the 3D incompressible Euler equations. We prove that finite kinetic energy of the initial data implies the similarity exponent γ satisfies γ > 2/5. If a smooth globally self-similar blow-up profile exists and satisfies an outgoing condition, then γ ≥ 1/2. […] |
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Title: The Fano of lines and the Kuznetsov component of cubic fourfoldsAbstract: A smooth cubic fourfold gives rise to two kinds of hyperkähler fourfolds: one is classical --the variety of lines on the cubic; and the other is "non-commutative" --arising from the symmetric square of the Kuznetsov component. Galkin conjectured that these two objects should be derived […] |
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Title: Eigenvarieties over CM fields and Galois representationsAbstract: Eigenvarieties are parameter spaces for certain p-adic automorphic forms of varying weight. These objects have become increasingly popular for studying the Fontaine—Mazur conjecture, which leads us to ask what kinds of Galois representations appear on eigenvarieties. Our main result shows that for eigenvarieties for the group GL_n […] |
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Title: The Harnack inequality without convexity for the Curve Shortening Flow Abstract: Everything I will discuss is joint work with P. M. Topping. In 1995, Hamilton introduced a Harnack inequality for convex solutions of the Mean Curvature Flow. Hamilton’s Harnack Inequality has played an important role in the theory of the Curve Shortening Flow (CSF), for […] |
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