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BEGIN:VEVENT
UID:0fee14031f4a8f23858e730c5f732bb4
CATEGORIES:Colloquia
CREATED:20250115T150427
SUMMARY:Colloquium: Jonathan Tidor - Discrete geometry via semialgebraic graphs
LOCATION:Hill 705
DESCRIPTION:<p><span style="font-style: normal; font-weight: 400; letter-spacing: norma
 l; text-align: start; text-indent: 0px; text-transform: none; white-space: 
 normal; word-spacing: 0px; text-decoration: none; color: #000000; font-fami
 ly: RobotoMono-Regular; font-size: 14px; float: none;">Speaker: Jonathan Ti
 dor, Stanford University</span><br style="font-style: normal; font-weight: 
 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-tran
 sform: none; white-space: normal; word-spacing: 0px; text-decoration: none;
  color: #000000; font-family: RobotoMono-Regular; font-size: 14px;"><br sty
 le="font-style: normal; font-weight: 400; letter-spacing: normal; text-alig
 n: start; text-indent: 0px; text-transform: none; white-space: normal; word
 -spacing: 0px; text-decoration: none; color: #000000; font-family: RobotoMo
 no-Regular; font-size: 14px;"><span style="font-style: normal; font-weight:
  400; letter-spacing: normal; text-align: start; text-indent: 0px; text-tra
 nsform: none; white-space: normal; word-spacing: 0px; text-decoration: none
 ; color: #000000; font-family: RobotoMono-Regular; font-size: 14px; float: 
 none;">Title: Discrete geometry via semialgebraic graphs</span><br style="f
 ont-style: normal; font-weight: 400; letter-spacing: normal; text-align: st
 art; text-indent: 0px; text-transform: none; white-space: normal; word-spac
 ing: 0px; text-decoration: none; color: #000000; font-family: RobotoMono-Re
 gular; font-size: 14px;"><br style="font-style: normal; font-weight: 400; l
 etter-spacing: normal; text-align: start; text-indent: 0px; text-transform:
  none; white-space: normal; word-spacing: 0px; text-decoration: none; color
 : #000000; font-family: RobotoMono-Regular; font-size: 14px;"><span style="
 font-style: normal; font-weight: 400; letter-spacing: normal; text-align: s
 tart; text-indent: 0px; text-transform: none; white-space: normal; word-spa
 cing: 0px; text-decoration: none; color: #000000; font-family: RobotoMono-R
 egular; font-size: 14px; float: none;">Abstract:<br></span><br style="font-
 style: normal; font-weight: 400; letter-spacing: normal; text-align: start;
  text-indent: 0px; text-transform: none; white-space: normal; word-spacing:
  0px; text-decoration: none; color: #000000; font-family: RobotoMono-Regula
 r; font-size: 14px;"><span style="font-style: normal; font-weight: 400; let
 ter-spacing: normal; text-align: start; text-indent: 0px; text-transform: n
 one; white-space: normal; word-spacing: 0px; text-decoration: none; color: 
 #000000; font-family: RobotoMono-Regular; font-size: 14px; float: none;">Ma
 ny problems in discrete geometry can be naturally encoded by a graph. Using
  tools from graph theory then gives information about the original geometri
 c problem. In recent years, this paradigm has been strengthened by noting t
 hat, in many cases of interest, the corresponding graph is in the class of 
 so-called "semialgebraic graphs". Proving strong results on the structure o
 f semialgebraic graphs then immediately has many consequences back in the g
 eometric setting. Semialgebraic graphs are useful for studying a number of 
 problems including the Erdős unit distance problem and many of its variants
 , point-line incidence problems studied by Szemerédi–Trotter and by Guth–Ka
 tz, general problems about incidences of varieties, and many more examples.
 </span><br style="font-style: normal; font-weight: 400; letter-spacing: nor
 mal; text-align: start; text-indent: 0px; text-transform: none; white-space
 : normal; word-spacing: 0px; text-decoration: none; color: #000000; font-fa
 mily: RobotoMono-Regular; font-size: 14px;"><br style="font-style: normal; 
 font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0
 px; text-transform: none; white-space: normal; word-spacing: 0px; text-deco
 ration: none; color: #000000; font-family: RobotoMono-Regular; font-size: 1
 4px;"><span style="font-style: normal; font-weight: 400; letter-spacing: no
 rmal; text-align: start; text-indent: 0px; text-transform: none; white-spac
 e: normal; word-spacing: 0px; text-decoration: none; color: #000000; font-f
 amily: RobotoMono-Regular; font-size: 14px; float: none;">In this talk, I w
 ill introduce some problems in discrete geometry and define semialgebraic g
 raphs. Then I will discuss a number of new structural and extremal results 
 about semialgebraic graphs and the geometric consequences of these results.
  These include a regularity lemma with asymptotically optimal bounds and an
  improvement on the Zarankiewicz problem for semialgebraic graphs. These re
 sults are proved via a novel extension of the polynomial method, building u
 pon the polynomial partitioning machinery of Guth–Katz and Walsh.</span><br
  style="font-style: normal; font-weight: 400; letter-spacing: normal; text-
 align: start; text-indent: 0px; text-transform: none; white-space: normal; 
 word-spacing: 0px; text-decoration: none; color: #000000; font-family: Robo
 toMono-Regular; font-size: 14px;"><br style="font-style: normal; font-weigh
 t: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-t
 ransform: none; white-space: normal; word-spacing: 0px; text-decoration: no
 ne; color: #000000; font-family: RobotoMono-Regular; font-size: 14px;"><spa
 n style="font-style: normal; font-weight: 400; letter-spacing: normal; text
 -align: start; text-indent: 0px; text-transform: none; white-space: normal;
  word-spacing: 0px; text-decoration: none; color: #000000; font-family: Rob
 otoMono-Regular; font-size: 14px; float: none;">Based on joint work with Hu
 ng-Hsun Hans Yu.</span></p>
CONTACT:Jonathan Tidor
DTSTAMP:20260827T220207
DTSTART;TZID=America/New_York:20250121T140000
DTEND;TZID=America/New_York:20250121T150000
SEQUENCE:0
TRANSP:OPAQUE
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