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DTSTART;TZID=America/New_York:20230302T120000
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DTSTAMP:20260411T063920
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UID:10001235-1677758400-1677762000@cmsa.fas.harvard.edu
SUMMARY:New bounds on lattice covering volumes\, and nearly uniform covers
DESCRIPTION:Member Seminar \nSpeaker: Barak Weiss   \nTitle: New bounds on lattice covering volumes\, and nearly uniform covers \nAbstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K 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 translates of K\, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem\, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE\, Hebrew University) and Oded Regev (CS\, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper\, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-3223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
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DTSTART;TZID=America/New_York:20230302T160000
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LAST-MODIFIED:20240216T085143Z
UID:10001276-1677772800-1677776400@cmsa.fas.harvard.edu
SUMMARY:The string/black hole transition in anti de Sitter space
DESCRIPTION:Speaker: Erez Urbach\, Weizmann Institute of Science \nTitle: The string/black hole transition in anti de Sitter space \nAbstract: String stars\, or Horowitz-Polchinski solutions\, are string theory saddles with normalizable condensates of thermal-winding strings. In the past\, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime\, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux)\, their possible connection to small black holes in AdS\, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model\, and their relation to the deconfined phase of 3+1 pure Yang-Mills.
URL:https://cmsa.fas.harvard.edu/event/collquium-3223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
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