Upcoming Events
Abstract TBA
We care about arithmetic invariants of polynomial equations / motives e.g. conductors or L-functions, which (conjecturally) are often automorphic and related to cycles on Shimura varieties. In this talk, I will focus on L-functions of Asai motives (e.g. Rankin-Selberg motives for GL_n x GL_n)…
Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology(LCH) for Rizell-Golovko's lifted Legendrians…
I will talk about how critical multiplicative chaos in probability theory is connected to and leads to recent breakthroughs in probabilistic number theory, in particular, the study of random multiplicative functions and character sums. No background in number theory is assumed.
Knot invariants are typically used to give a negative answer to the question of when two embeddings are ambiently isotopic, and rarely to give a positive answer. An exception is the celebrated result of Freedman and Quinn that if the complement of a 2-sphere embedded in the 4-sphere has…
In this talk, we shall discuss our recent work which shows that in the periodic homogenization of viscous HJ equations in any spatial dimension the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original Hamiltonian. Moreover,…
Quantum unique ergodicity (QUE) describes the equidistribution of the L2-mass of eigenfunctions of the Laplacian as their eigenvalues approach infinity. My focus lies on a specific variant known as holomorphic QUE, which concerns the distribution of the L2-mass of normalized…
Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemerédi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.In this talk, we shall discuss various…
Spection 4, 5.1 of [FP97].
We will move from the local to the global theory of FIOs, providing invariant definitions of relevant notions such as operator symbols. The necessary tools from symplectic geometry will be introduced. If time permits, we'll begin considering some applications.