[Colloquium] [Theory] TODAY at 10am: 4/27 Young Researcher Seminar Series: Max Hopkins, UC San Diego

[Mary Marre]

*When:*        Wednesday, April 27th at* 10:00 am CT*


*Where:       *Talk will be given *live, in-person* at

                   TTIC, 6045 S. Kenwood Avenue

                   5th Floor, Room 530


*Where:*       Zoom Virtual Talk (*register in advance here
<https://uchicagogroup.zoom.us/webinar/register/WN_2kc9JA-KQl-jZgl3lXUJYw>*)


*Who: *         Max Hopkins, UC San Diego


*Title*: Hypercontractivity and Small-Set Expansion on High Dimensional
Expanders.

*Abstract*: Hypercontractivity is one of the most powerful tools in Boolean
function analysis. Traditionally studied on the Boolean cube, recent years
have seen a number of exciting applications of hypercontractivity on
extended domains, most famously including the resolution of Khot’s 2-2
games conjecture. Unfortunately, beyond a few known examples our general
understanding of hypercontractivity actually remains remarkably poor,
severely limiting further avenues of application.

In this talk, we discuss the first steps towards a unified theory of
hypercontractivity based on *high dimensional expanders* (HDX), a broad
class of hypergraphs that have recently seen a series of breakthrough
applications in coding theory and approximate sampling. Throughout the
talk, we’ll pay special attention to the motivating application of
characterizing small-set expansion in graphs, and briefly discuss how the
line of work could lead to new insights towards resolving the unique games
conjecture.

Based on joint work with Mitali Bafna, Tali Kaufman, and Shachar Lovett to
appear at STOC 2022.

*Bio: *Max Hopkins is a fourth year PhD Student at UC San Diego. He is an
NSF GRFP fellow and an ARCS scholar, and holds a B.A. in mathematics from
Harvard University. Max is broadly interested in understanding the role of
mathematical structure in computation. Currently he works mostly on
developing the theory of high dimensional expansion and its role in
hardness of approximation, and on the development and application of
combinatorial and geometric techniques in learning theory.

*Host: **Madhur Tulsiani* <madhurt at ttic.edu>
Mary C. Marre
Faculty Administrative Support
*Toyota Technological Institute*
*6045 S. Kenwood Avenue*
*Chicago, IL  60637*
*mmarre at ttic.edu <mmarre at ttic.edu>*


On Tue, Apr 26, 2022 at 3:32 PM Mary Marre <mmarre at ttic.edu> wrote:

> *When:*        Wednesday, April 27th at* 10:00 am CT*
>
>
> *Where:       *Talk will be given *live, in-person* at
>
>                    TTIC, 6045 S. Kenwood Avenue
>
>                    5th Floor, Room 530
>
>
> *Where:*       Zoom Virtual Talk (*register in advance here
> <https://uchicagogroup.zoom.us/webinar/register/WN_2kc9JA-KQl-jZgl3lXUJYw>*
> )
>
>
> *Who: *         Max Hopkins, UC San Diego
>
>
> *Title*: Hypercontractivity and Small-Set Expansion on High Dimensional
> Expanders.
>
> *Abstract*: Hypercontractivity is one of the most powerful tools in
> Boolean function analysis. Traditionally studied on the Boolean cube,
> recent years have seen a number of exciting applications of
> hypercontractivity on extended domains, most famously including the
> resolution of Khot’s 2-2 games conjecture. Unfortunately, beyond a few
> known examples our general understanding of hypercontractivity actually
> remains remarkably poor, severely limiting further avenues of application