On the topology and index of minimal surfaces

Davi Maximo
University of Pennsylvania; Member, School of Mathematics
February 5, 2019
For an immersed minimal surface in $R^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously obtained bounding the genus and number of ends by the index. Our new estimate resolves several conjectures made by J. Choe and D.

Near-Optimal Strong Dispersers

Dean Doron
The University of Texas at Austin
February 4, 2019

Randomness dispersers are an important tool in the theory of pseudorandomness, with numerous applications. In this talk, we will consider one-bit strong dispersers and show their connection to erasure list-decodable codes and Ramsey graphs. 

The Sample Complexity of Multi-Reference Alignment

Philippe Rigollet
Massachusetts Institute of Technology; Visiting Professor, School of Mathematics
February 4, 2019
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown cyclic shifts? This simple problem has surprisingly broad applications, in fields from aircraft radar imaging to structural biology with the ultimate goal of understanding the sample complexity of Cryo-EM. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations.

Drinfeld's lemma for schemes

Kiran Kedlaya
University of California, San Diego; Visiting Professor, School of Mathematics
February 4, 2019
In the course of constructing the Langlands correspondence for GL(2) over a function field, Drinfeld discovered a surprising fact about the interaction between étale fundamental groups and products of schemes in characteristic p. We state this result, describe a new approach to it involving a generalization to perfectoid spaces, and mention an application in p-adic Hodge theory (from joint work with Carter and Zabradi).

Academic Publishing: An Insider’s View

Fred Appel, Princeton University Press (Executive Editor Anthropology and Religion) Eric Henney, Basic Books (Editor) Gillian Greenough, Wiley (Executive Editor, Life and Physical Sciences) Eric Crahan, Princeton University Press (Executive Editor for His
February 1, 2019

Princeton University Press will spearhead a discussion with others in the publishing realm on the current and future state of academic publishing.
 

Dilworth Room, Simons Hall 12-2:00 p.m.
Suggested Audience: IAS Members and Visitors and partners/spouses
Lunch will be provided. To register, click HERE.

Upper bounds for constant slope p-adic families of modular forms

John Bergdall
Bryn Mawr College
January 31, 2019
This talk is concerned with the radius of convergence of p-adic families of modular forms --- q-series over a p-adic disc whose specialization to certain integer points is the q-expansion of a classical Hecke eigenform of level p. Numerical experiments by Gouvêa and Mazur in the nineties predicted the general existence of such families but also suggested, in spirit, the radius of convergence in terms of an initial member. Buzzard and Calegari showed, ten years later, that the Gouvêa--Mazur prediction was false. It has since remained open question how to salvage it.

Analyticity results for the Navier-Stokes Equations

Guher Camliyurt
Member, School of Mathematics
January 31, 2019
We consider the Navier–Stokes equations posed on the half space, with Dirichlet boundary conditions. We give a direct energy based proof for the instantaneous space-time analyticity and Gevrey class regularity of the solutions, uniformly up to the boundary of the half space. We then discuss the adaptation of the same method for bounded domains.

Minmax minimal surfaces in arbitrary codimension with

Tristan Rivière
ETH Zürich; Member, School of Mathematics
January 29, 2019

We shall present a procedure which to any admissible family
of immersions
of surfaces into an arbitrary closed riemannian manifolds assigns a
smooth, possibly branched, minimal surface
whose area is equal to the width of the corresponding minmax and whose
Morse index is bounded by the
dimension of the familly. We will discuss the question of bounding the
Morse index + Nullity from below as well as possible extensions of
this procedure to more general families.