Seminars Sorted by Series

Abstract: We prove an ordinary modularity lifting theorem for certain non-regular 4-dimensional symplectic representations over totally real fields. The argument uses both higher Hida theory and the Calegari-Geraghty version of the Taylor-Wiles...

Abstract: We will discuss joint work with Calegari, Caraiani, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne that proves potential automorphy of symmetric powers of rank two compatible systems of weight zero. As a consequence, we deduce the...

Abstract: Wiles' work on modularity of elliptic curves over the rationals, used as a starting point that odd, irreducible represenations $G_Q \rightarrow GL_2 (F_3)$ arise from cohomological cusp forms (i.e. new forms of weight $K \geq 2$).In...

Abstract: I will discuss a recent conjecture formulated in an ongoing project with Jan Vonk relating the intersection numbers of one-dimensional topological cycles on certain Shimura curves to the arithmetic intersections of associated real...

Abstract: Euler systems are compatible families of cohomology classes for a global Galois represenation, which plan an important role in studying Selmer groups. I will outline the construction of a new Euler system, for the Galois representation...

Abstract: Given a p-adic reductive group G and its (pro-p) Iwahori-Hecke algebra H, we are interested in the link between the category of smooth representations of G and the category of H-modules. When the field of coefficients has characteristic...

Abstract: In his ladmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. We use deformation theory of pseudorepresentations to study...

Abstract: In his classical work, Mazur considers the Eisenstein ideal $I$ of the Hecke algebra $\mathbb{T}$ acting on cusp forms of weight $2$ and level $\Gamma_0(N)$ where $N$ is prime. When $p$ is an Eisenstein prime, i.e. $p$ divides the...

Abstract: Zywina showed that after passing to a suitable field extnesion, every abelian surface $A$ with real multiplication over some number field has geometrically simple reduction modulo $\frak{p}$ for a density one set of primes $\frak{p}$. One...

Abstract: An important input into modularity lifting theorems is an understanding of the geometry of Galois deformation rings, especially local deformation rings with p-adic Hodge theory conditions at $\ell=p$. Outside of a few cases (ordinary...

Abstract: A rather notorious mistake occurs p. 217 in the proof of Lemma 6.3 of the book "Simple algebras, base change, and the advanced theory of the trace formula" (1989) by J. Arthur, L. Clozel. E. Lapid and J. Rogawski (1998) proposed a proof of...

Abstract: We prove that the weight 4 Beilinson's regulator map can be expressed via the classical n-logarithms, $n \leq 4$. This plus Borel's theorem implies Zagier's conjecture, relating the value of the Dedekind zeta functions at $s=4$ and the...

Deep learning has led to rapid progress being made in the field of machine learning and artificial intelligence, leading to dramatically improved solutions of many challenging problems such as image understanding, speech recognition, and control...

Few-shot classification, the task of adapting a classifier to unseen classes given a small labeled dataset, is an important step on the path toward human-like machine learning. I will present some of the key advances in this area, and will then...

Genomics has revolutionized biology, enabling the interrogation of whole transcriptomes, genome-wide binding sites for proteins, and many other molecular processes. However, individual genomic assays measure elements that interact in vivo as...

Existing generative models are typically based on explicit representations of probability distributions (e.g., autoregressive or VAEs) or implicit sampling procedures (e.g., GANs). We propose an alternative approach based on modeling directly the...

In this talk, I would like to share some of my reflections on the progress made in the field of interpretable machine learning. We will reflect on where we are going as a field, and what are the things that we need to be aware of to make progress...

Implicit generative models such as GANs have achieved remarkable progress at generating convincing fake images, but how well do they really match the distribution? Log-likelihood has been used extensively to evaluate generative models whenever it’s...

While the trend in machine learning has tended towards more complex hypothesis spaces, it is not clear that this extra complexity is always necessary or helpful for many domains. In particular, models and their predictions are often made easier to...

In this talk, I will first introduce our recent work on the Deep Equilibrium Model (DEQ). Instead of stacking nonlinear layers, as is common in deep learning, this approach finds the equilibrium point of the repeated iteration of a single non-linear...

Despite the success of deep learning, much of its success has existed in settings where the goal is to learn one, single-purpose function from data. However, in many contexts, we hope to optimize neural networks for multiple, distinct tasks (i.e...

Physical processes in the world often have a modular structure, with complexity emerging through combinations of simpler subsystems. Machine learning seeks to uncover and use regularities in the physical world. Although these regularities manifest...

Standard machine learning produces models that are highly accurate on average but that degrade dramatically when the test distribution deviates from the training distribution. While one can train robust models, this often comes at the expense of...

There are several broad insights we can draw from computational models of human cognition in order to build more human-like forms of machine learning. (1) The brain has a great deal of built-in structure, yet still tremendous need and potential for...

We are interested in moments of velocity increments and derivatives, characterized by scaling exponents overline{(v(x + r) − v(x))n} ∝ r^ζn and overline{(∂xvx)n} ∝ Re^ρn , respectively. In high Reynolds number flows, the moments of different orders...

Abstract: The confounding question of asymptotically high Rayleigh number heat transport in Rayleigh-Bénard convection modeled by the Boussineq approximation to the Navier-Stokes equations is reviewed from viewpoints of theory (models of the model)...

Abstract: I will discuss some preliminary work on using machine learning
to produce turbulence models that can be used in large eddy simulation.
I will discuss how better models can be constructed and in general,
how one can use machine learning to...

5 minutes each:Steve Childress (NYU)Camillo de Lellis (IAS)Yakov Sinai (Princeton University/IAS)Jalal Shatah (NYU)Larry Sirovich (Rockefeller)John Wettlaufer (Yale University)

Abstract: I will discuss the recent non-uniqueness result with Vlad Vicol on the non-uniqueness of weak solutions to the Navier-Stokes equations, as well as the follow up paper by myself, Maria Colombo and Vicol. I hope to phrase the results within...

Abstract: We consider a class of dynamical systems described by ordinary differential equations with an isolated singularity, where the singularity is characterized by the lack of Lipschitz continuity. Singularities are common in applications both...

Abstract: The purpose of this work is to perform a mathematically rigorous study of Lagrangian chaos and "passive scalar turbulence" in incompressible fluid mechanics. We study the Lagrangian flow map associated to 2D Navier-Stokes and hyper-viscous...

Abstract: I will present a new approach to the isometric embedding problem. The main new idea is to use the theory of stochastic flows in combination with various possible gradient flow structures. These ideas are motivated by the statistical...