Special Points on Moduli Spaces
Explore the distribution of special points in moduli spaces, examining algebraic and analytic aspects, including the Andre-Oort conjecture and p-adic distribution.
Real Groups, Symmetric Varieties and Langlands Duality - ICBS 2024
Explore connections between relative Langlands duality and geometric Langlands for real groups, examining derived Satake equivalence for symmetric varieties.
New Frontiers in Structure vs Randomness with Applications to Combinatorics, Complexity, and Algorithms
Explore new frontiers in structure vs randomness, delving into applications in combinatorics, complexity, and algorithms. Gain insights on Erdos-Turan problem and recent advancements in additive combinatorics.
Around the Alexandrov-Fenchel Inequality - Convex Geometry and Its Applications
Explore the history and recent progress in convex geometry, focusing on Minkowski's theory and its connections to various mathematical disciplines.
Sparsity of Rational Points on Curves - What is Known and What is Expected
Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.
Eisenstein Series - An Overview
Explore Eisenstein series in a concise, self-contained overview, gaining insights into this mathematical concept and its applications.
On the p-adic Local Langlands Correspondence
Explore the $p$-adic local Langlands correspondence for ${\mathrm GL}_2({\mathbb Q}_p)$, focusing on geometric constructions from joint works with Dospinescu and Niziol.
The Langlands Project - Connecting Automorphic Forms and Number Theory
Explore the Langlands project's deep connection between automorphic forms and arithmetic, tracing its roots and current challenges in mathematics.
Low Moments of Character Sums - ICBS 2024
Explore low moments of character sums, comparing Dirichlet characters to random multiplicative functions and discussing potential applications to non-vanishing.
Open Problems in Diophantine Approximation and Geometry of Numbers
Explore open problems in Diophantine Approximation and Geometry of Numbers, focusing on approximation of subspaces in R^d by rational subspaces and related mathematical concepts.
Geometry and Integers - Connections Between Number Theory and Geometric Structures
Explore connections between non-negative integer sets and diverse geometries, examining functions associated with primitive integer vectors and their relation to convex, toric, and birational geometries.
Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications
Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.
Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds
Explore Donaldson-Thomas invariants, their connection to BPS indices, and modular behavior in string theory. Gain insights into computational methods and applications to Gopakumar-Vafa invariants and topological string amplitudes.
Homological Aspects of Branching Laws in p-adic Groups
Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
The Local Langlands Program and Characteristic p
Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
Branching Processes in Random Matrix Theory and Analytic Number Theory
Explore branching processes in random matrix theory and analytic number theory, focusing on limiting distributions, log-correlated phenomena, and recent conjectures about maxima of characteristic polynomials and L-functions.
Resolution of the Quadratic Littlewood-Offord Problem
Explore the resolution of the Quadratic Littlewood-Offord problem with expert Mathew Kwan, delving into combinatorics and its probabilistic connections.
On the Erdös-Ginzburg-Ziv Problem in Large Dimension
Explore the Erdös-Ginzburg-Ziv Problem in high dimensions with Professor Lisa Sauermann, delving into advanced combinatorics and number theory concepts.
Spherical Functions and Mirror Symmetry
Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.
Dense Embeddings of Hyperbolic Manifold Groups
Explore dense embeddings of hyperbolic manifold groups, focusing on amalgamated products and linear Lie groups. Learn strategies to control properties of output embeddings.