## Distinguished Lecture Series

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.

*Previous speakers of the DLS include:* Peter Sarnak, Peter Schneider, Zhengan Weng, Etienne Ghys, Goro Shimura, Jean Bellissard, Andrei Suslin, Pierre Deligne, Michael Harris, Alexander Lubotzky, Shing-Tau Yau, Hillel Furstenberg, Robert R. Langlands, Clifford Taubes, Louis Nirenberg, Oded Schramm, Louis Nirenberg, I.M. Singer, Jesper Lutzen, L.H. Eliasson, Raoul Bott, Dennis Gaitsgory, Gilles Pisier, Gregg Zuckerman, Freydoon Shahidi, Alain Connes, Jöran Friberg, David Mumford, Sir Michael Atiyah, Jean-Michel Bismut, Jean-Pierre Serre, G. Tian, N. Sibony, C. Deninger, Peter Lax, and Nikolai Reshetikhin.

**The DLS is currently supported by the Larry M. Wiener fund.**

## Past Lectures

University of Strasbourg Visit: 04/03/2013 to 04/20/2013 |
Rheinische Friedrich-Wilhelms-Universität Bonn Visit: 05/07/2013 to 05/09/2013 |
Eötvös Loránd University Visit: 05/28/2013 to 05/30/2013 |

Texas A&M Visit: 10/22/2013 to 10/26/2013 |
IAS, Princeton Visit: 10/30/2013 to 11/06/2013 |
Duke University / UC Berkeley Visit: 05/19/2014 to 05/23/2014 |

Cambridge University Visit: 10/04/2014 to 10/10/2014 |
Microsoft Research Visit: 11/03/2014 to 11/06/2014 |
Columbia University Visit: 02/17/2015 to 02/19/2015 |

Princeton University Visit: 05/19/2015 to 05/21/2015 |

## Upcoming Lectures

### Benedict Gross

#### Harvard University

**Visit:**04/25/2016 to 04/28/2016

**Lectures:**

**Tuesday, April 26th; 3:00 pm MS 6627**

**The rank of elliptic curves**

Elliptic curves, or cubic equations in two variables, have been a central object of study in number theory since the time of Fermat. The set of their rational points forms an abelian group, which Mordell proved was finitely generated. Many of the interesting open questions in the field concern the rank of this group. In this talk, I will review the conjecture of Birch and Swinnerton-Dyer, and summarize the progress that has been made in the direction of a proof. I will also discuss approaches to study the average rank, for all elliptic curves over Q.

**Wednesday, April 27th; 3:00 pm MS 6627**

**The arithmetic of hyperelliptic curves**

Hyperelliptic curves first appeared in the work of Abel on integration, where he defined their genus g. Every such curve of genus g has an affine equation of the form y^2 = F(x), where F(x) is a separable polynomial of degree 2g+2. Abel and his contemporaries studied these curves over the real and complex numbers; in this talk I will focus on the case when the curve is defined over the rational numbers (or equivalently, when the polynomial F(x) has rational coefficients). In that case, an important invariant is the set of rational solutions. When the genus is at least 2, Faltings proved that this set is finite. In fact, one can now show that this set is usually empty, and in many cases, there are no solutions over any odd degree extension of Q.

**Thursday, April 28th; 4:15 pm MS 6627**

**Pencils of quadrics and the Jacobians of hyperelliptic curves**

Beyond linear subspaces in projective space, the next simplest subvarieties are quadrics, which are the hypersurfaces of degree 2. These are easily classified by a discrete invariant (the rank) over the complex numbers, but once one takes a pair of quadrics, given by two symmetric matrices A and B, the situation becomes more interesting. The most general pencils Ax - By are those where the binary form det(Ax - By) has a non-zero discriminant. I will discuss how this theory is related to certain coverings of the Jacobians of hyperelliptic curves, and how pencils can be used to study the arithmetic of the curve.

#### About Benedict Gross:

**Poster:** GROSS.pdf

### Donald Goldfarb

#### Columbia University

**Visit:**05/17/2016 to 05/19/2016

**Lectures:**

**Optimization for Learning and Big Data**

**Abstract**: Many problems in both supervised and unsupervised machine learning (e.g., logistic regression, support vector machines, deep neural networks, robust principal component analysis, dictionary learning, latent variable models) and signal processing (e.g., face recognition and compressed sensing) are solved by optimization and related algorithms. In today's age of big data, the size of these problems is often formidable. E.g., in logistic regression the objective function may be expressed as the sum of ~10^9 functions (one for each data point) involving ~10^6 variables (features). In this series of talks, we will review current optimization approaches for addressing this challenge from the following classes of methods: first-order (and accelerated variants), stochastic gradient and second-order extensions, alternating direction methods for structured problems (including proximal and conditional gradient and multiplier methods), tensor decomposition, randomized methods for linear systems, and parallel and distributed variants.

**Lecture 1: Tuesday, May 17; 3:00 pm, MS 6627**

**Lecture 2: Wednesday, May 18; 3:00 pm, MS 6627**

**Lecture 3: Thursday, May 19; 3:00 pm, MS 6627 **

#### About Donald Goldfarb:

**Poster:** GOLDFARB.Final_.pdf