CS Events

Computer Science Department Colloquium Geometry, Arithmetic and Computation of Polynomials
Export Event Save iCal Send to Google Calendar Send to Yahoo Calendar Send to Outlook Live Send to Microsoft Outlook Save iCal Preserve formatting in description (only supported in some calendar applications) Close Thursday, January 25, 2024, 10:30am - 11:30am

Speaker: Akash Kumar Sengupta

Bio

Akash Kumar Sengupta is a postdoctoral fellow in the Department of Mathematics and a member of the Algorithms & Complexity group at the University of Waterloo. Previously, he was a J. F. Ritt Assistant Professor at Columbia University. He received his PhD in Mathematics from Princeton University in 2019, advised by János Kollár. He is broadly interested in theoretical computer science, algebraic geometry, number theory and their interconnections. In particular, his research in algebraic complexity theory has focused on the Polynomial Identity Testing (PIT) problem. Two prominent highlights of his research are: the solution to Gupta’s radical Sylvester-Gallai conjecture for obtaining PIT algorithms, and the solution to the geometric consistency problem of Manin’s conjecture.

Location : CoRE 301

: 

Event Type: Computer Science Department Colloquium

Abstract: Polynomials are ubiquitous in various branches of mathematics and sciences ranging from computer science to number theory. A remarkable phenomenon is that the algebraic-geometric properties of polynomials govern their arithmetic and computational behavior. As a result, algebraic-geometric techniques have led to exciting progress towards fundamental problems in complexity theory and number theory. I’ll begin with an overview of my research in these areas, including the problems of counting rational solutions and efficient computation of polynomials. Then, we will dig deeper into the Polynomial Identity Testing (PIT) problem, a central problem in computational complexity. PIT has applications to a wide range of problems, such as circuit lower bounds, perfect matching and primality testing. In this talk, I’ll discuss an algebraic-geometric approach towards polynomial-time deterministic algorithms for PIT via Sylvester-Gallai configurations. In particular, we will see that dimension bounds on SG-configurations yield poly-time PIT algorithms. I’ll talk about my work on the geometry of SG-configurations, showing that radical SG-configurations are indeed low-dimensional, as conjectured by Gupta in 2014.

: 

Contact  Prof. Mario Szegedy

Join Zoom Meeting
https://rutgers.zoom.us/j/91695459936?pwd=SDUreXB1cFNTRk5FUWQ1c3ZhWnhVUT09
Join by SIP
Meeting ID: 916 9545 9936
Password: 476228