The covering volume of lattices, and nearly uniform coverings (1/3)

by Prof. Barak Weiss (Tel Aviv University)

Tuesday 18 Oct 2022, 10:00 → 11:00 Asia/Kolkata

AG-66,AG-69,AG77

Dear all, Professor Barak Weiss from Tel Aviv University will give a series of three lectures. The details are below. Time and Venue Lecture 1: 10:00 am to 11:00 am October 18, AG–66 Lecture 2: 4:00 pm to 5:00 pm October 19, AG–69 Lecture 3: 4:00 pm to 5:00 pm October 21, AG–77 Title: The covering volume of lattices, and nearly uniform coverings Abstract: Let L in R^n be a lattice and let K be a convex body. The covering volume of K w.r.t. L is the minimal volume of a dilate rK such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by copies of K, translated by elements of L. Finding upper bounds on the covering volume as the dimension n goes to infinity, is a well-studied problem, with connections to practical issues arising in computer science and electrical engineering. In a recent paper with Ordentlich (EE, Hebrew U) and Regev (CS, NYU), we obtain substantial improvements to bounds of Rogers from the 1950’s. In another recent paper, we obtain bounds on the minimal volume of nearly uniform covers, where a pair (L, K) give an epsilon-nearly uniform cover if the ratio between max_x |{l in L : x in l+K}| and min_y |{l in L : y in l+K}| is at most 1+epsilon. The key to these results are recent breakthroughs due to Dvir and others regarding the discrete Kakeya problem. I will give three lectures about these results, including history, applications, and some ideas of the proofs. No prerequisites beyond undergraduate material (measures, volumes, vector spaces over finite fields) will be assumed. ----------------------------------------------------- YouTube live link: 18-10-2022 --> https://youtu.be/029xTLyiNbw 19-10-2022 --> https://youtu.be/jW3ZTdpQPl4 21-10-2022 --> https://youtu.be/iwQAOaM5Mbw ------------------------------------------------------ Tifrmum_ vc5 is inviting you to a scheduled Zoom meeting. Topic: The Infosys Chandrasekharan Random Geometry Lecture Series Join Zoom Meeting https://tifr-res-in.zoom.us/j/92151898634 Meeting ID: 921 5189 8634 Passcode: 361136 ---------------------------------------------------------

Poster Barak_Weiss.pdf