## The amazing power of composition

Toniann Pitassi

University of Toronto

October 8, 2016

Schedule: https://www.math.ias.edu/avi60/agenda

Yve-Alain Bois

Pablo Picasso did not speak often about abstraction, but when he did, it was either to dismiss it as complacent decoration or to declare its very notion an oxymoron. The root of this hostility is to be found in the impasse that the artist reached in the summer 1910, when abstraction suddenly appeared as the logical development of his previous work, a possibility at which he recoiled in horror. But though he swore to never go again near abstraction, he could not prevent himself from testing his... Read more

Toniann Pitassi

University of Toronto

October 8, 2016

Schedule: https://www.math.ias.edu/avi60/agenda

Scott Ransom

National Radio Astronomy Observatory

November 22, 2016

Zeyuan Allen-Zhu

Member, School of Mathematics

November 22, 2016

In this talk I will show how to derive the fastest coordinate descent method [1] and the fastest stochastic gradient descent method [2], both from the linear-coupling framework [3]. I will relate them to linear system solving, conjugate gradient method, the Chebyshev approximation theory, and raise several open questions at the end. No prior knowledge is required on first-order methods.

Florian Sprung

Princeton University; Visitor, School of Mathematics

November 21, 2016

Computing the class number is a hard question. In 1956, Iwasawa announced a surprising formula for an infinite family of class numbers, starting an entire theory that lies behind this phenomenon. We will not focus too much on this theory (Iwasawa theory), but rather describe some analogous formulas for modular forms. Their origins have not been explained yet, especially when the $p$-th Fourier coefficient is small.

Benjamin Elman

Princeton University

November 18, 2016

S.T. Lee Lecture: Philologists as Rogues?

Benjamin Elman, Gordon Wu ’58 Professor of Chinese Studies at Princeton University and former Mellon Visiting Professor (1999-2001) in the School of Historical Studies at the Institute, will deliver a public lecture, “Philologists as Rogues? The Life of a Confucian Classic Recovered in Early Modern Japan and Its Transmission Back to Imperial China,” on Friday, November 18, at 4:30 p.m. in West Lecture hall on the Institute campus.

Benjamin Elman, Gordon Wu ’58 Professor of Chinese Studies at Princeton University and former Mellon Visiting Professor (1999-2001) in the School of Historical Studies at the Institute, will deliver a public lecture, “Philologists as Rogues? The Life of a Confucian Classic Recovered in Early Modern Japan and Its Transmission Back to Imperial China,” on Friday, November 18, at 4:30 p.m. in West Lecture hall on the Institute campus.

Uri Feige

Weizmann Institute of Science

November 21, 2016

The random planted 3-coloring model generates a 3-colorable graph $G$ by first generating a random host graph $H$ of average degree $d$, and then planting in it a random 3-coloring (by giving each vertex a random color and dropping the monochromatic edges). For a sufficiently large constant $c$, Alon and Kahale [SICOMP 1997] presented a spectral algorithm that finds (with high probability) the planted 3-coloring of such graphs whenever $d > c\log n$.

Melanie Wood

University of Wisconsin–Madison

November 17, 2016

The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields. Since, by class field theory, the class group is the Galois group of the maximal unramified abelian extension, we can consider the Galois group of the maximal unramified extension as a non-abelian generalization of the class group. We will explain non-abelian analogs of the Cohen-Lenstra heuristics due to Boston, Bush, and Hajir and work, some joint with Boston, proving cases of the non-abelian conjectures in the function field analog.

Sergio Verdu

November 16, 2016

November 16, 2016