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UID:9d181537e3d78f9d96b2af1886be0dba
CATEGORIES:Colloquia
CREATED:20240212T161325
SUMMARY:Categorification and geometry
LOCATION:Hill 705
DESCRIPTION:Lars Hesselholt (IAS and Nagoya University)\nTitle: Categorification and ge
 ometryAbstract: The key principle in Grothendieck's algebraic geometry is t
 hat every commutative ring be considered as the ring of functions on some g
 eometric object. Clausen and Scholze have introduced a categorification of 
 algebraic and analytic geometry, where the key principle is that every stab
 le dualizably symmetric monoidal infinity-category be considered as the inf
 inity-category of quasi-coherent modules on some geometric object. In this 
 talk, I will explain this shift in paradigm as well as Clausen's philosophy
  that *every* cohomology theory should arise from this picture, complete wi
 th a six-functor formalism of categories of coefficients. The Hahn-Raksit-W
 ilson even filtration and Efimov continuity are key ingredients. \n
X-ALT-DESC;FMTTYPE=text/html:<p>Lars&nbsp;<span style="color: #000000; font-family: Aptos, Aptos_Embedde
 dFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 16px
 ; font-style: normal; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: start; text-indent: 0px; text-transform: none; widows: 2; word
 -spacing: 0px; white-space: normal; background-color: #ffffff; float: none;
 ">Hesselholt (IAS and&nbsp;<em style="font-weight: bold; font-style: normal
 ; color: #5f6368; font-family: Roboto, arial, sans-serif; font-size: 14px; 
 letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; tex
 t-transform: none; widows: 2; word-spacing: 0px; white-space: normal; backg
 round-color: #ffffff;">Nagoya</em><span style="color: #4d5156; font-family:
  Roboto, arial, sans-serif; font-size: 14px; font-style: normal; font-weigh
 t: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 
 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norma
 l; background-color: #ffffff; float: none;">&nbsp;University)</span></span>
 </p><div style="border: 0px; font-style: normal; font-weight: 400; font-siz
 e: 15px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West
  European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvet
 ica Neue', sans-serif; margin: 0px; padding: 0px; vertical-align: baseline;
  color: #242424; letter-spacing: normal; orphans: 2; text-align: start; tex
 t-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-sp
 ace: normal; background-color: #ffffff;"><span style="border: 0px; font-sty
 le: inherit; font-variant: inherit; font-weight: inherit; font-size: 15px; 
 line-height: inherit; font-family: inherit; margin: 0px; padding: 0px; vert
 ical-align: baseline;">Title: Categorification and geometry</span></div><di
 v style="border: 0px; font-style: normal; font-weight: 400; font-size: 15px
 ; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West Europe
 an)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neu
 e', sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; color:
  #242424; letter-spacing: normal; orphans: 2; text-align: start; text-inden
 t: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: no
 rmal; background-color: #ffffff;"><span style="border: 0px; font-style: inh
 erit; font-variant: inherit; font-weight: inherit; font-size: 15px; line-he
 ight: inherit; font-family: inherit; margin: 0px; padding: 0px; vertical-al
 ign: baseline;"></span></div><div style="border: 0px; font-style: normal; f
 ont-weight: 400; font-size: 15px; line-height: inherit; font-family: 'Segoe
  UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSy
 stemFont, Roboto, 'Helvetica Neue', sans-serif; margin: 0px; padding: 0px; 
 vertical-align: baseline; color: #242424; letter-spacing: normal; orphans: 
 2; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; wh
 ite-space: normal; text-align: left;"><span style="border: 0px; font-style:
  inherit; font-variant: inherit; font-weight: inherit; font-size: 15px; lin
 e-height: inherit; font-family: inherit; margin: 0px; padding: 0px; vertica
 l-align: baseline;">Abstract: The key principle in Grothendieck's algebraic
  geometry is that every commutative ring be considered as the ring of funct
 ions on some geometric object. Clausen and Scholze have introduced a catego
 rification of algebraic and analytic geometry, where the key principle is t
 hat every stable dualizably symmetric monoidal infinity-category be conside
 red as the infinity-category of quasi-coherent modules on some geometric ob
 ject. In this talk, I will explain this shift in paradigm as well as Clause
 n's philosophy that *every* cohomology theory should arise from this pictur
 e, complete with a six-functor formalism of categories of coefficients. The
  Hahn-Raksit-Wilson even filtration and Efimov continuity are key ingredien
 ts.</span></div><p>&nbsp;</p>
CONTACT:Lars Hesselholt (IAS and Nagoya University)
DTSTAMP:20260829T124617
DTSTART;TZID=America/New_York:20240221T153000
DTEND;TZID=America/New_York:20240221T163000
SEQUENCE:0
TRANSP:OPAQUE
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