BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20250428T140000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:90607d022d98b96073a22e20f68f6012 CATEGORIES:Algebra Seminar CREATED:20260429T111826 SUMMARY:Fake Projective Planes: From Existence to Explicit Equations LOCATION:Hill 705 DESCRIPTION:Since Mumford's 1979 construction proved the existence of fake projective p lanes, a natural problem has been to make these surfaces explicit: how can one actually write down defining equations for a fake projective plane? The history of this question passes through several major stages. First came M umford's original existential construction via p-adic uniformization. This was followed by the arithmetic classification program: results of Klingler and Yeung showed that fake projective planes are arithmetic ball quotients, while subsequent work of Prasad-Yeung and Cartwright-Steger reduced the po ssibilities to a complete list of 50 cases up to isomorphism of fundamental groups, or 100 up to bi-holomorphism. A new phase began when Borisov and K eum produced the first explicit equations for a fake projective plane, open ing the door to concrete geometric study of these surfaces. Since then, fur ther explicit constructions have been obtained by several authors. In this talk I will survey this development, explain the main ideas behind the pass age from existence to equations, and discuss possible interactions with fak e quadrics, which may be viewed as a degree-two analogue in the broader lan dscape of ``fake'' surfaces. A new phase began when Borisov and Keum produc ed the first explicit equations for a fake projective plane, opening the do or to concrete geometric study of these surfaces. Since then, further expli cit constructions have been obtained by several authors. In this talk I wil l survey this development, explain the main ideas behind the passage from e xistence to equations, and discuss possible interactions with fake quadrics , which may be viewed as a degree-two analogue in the broader landscape of ``fake'' surfaces.\n X-ALT-DESC;FMTTYPE=text/html:

Since Mumford's 1979 construction proved the existence of fake projectiv e planes, a natural problem has been to make these surfaces explicit: how c an one actually write down defining equations for a fake projective plane? The history of this question passes through several major stages. First cam e Mumford's original existential construction via p-adic uniformization. Th is was followed by the arithmetic classification program: results of Klingl er and Yeung showed that fake projective planes are arithmetic ball quotien ts, while subsequent work of Prasad-Yeung and Cartwright-Steger reduced the possibilities to a complete list of 50 cases up to isomorphism of fundamen tal groups, or 100 up to bi-holomorphism. A new phase began when Borisov an d Keum produced the first explicit equations for a fake projective plane, o pening the door to concrete geometric study of these surfaces. Since then, further explicit constructions have been obtained by several authors. In th is talk I will survey this development, explain the main ideas behind the p assage from existence to equations, and discuss possible interactions with fake quadrics, which may be viewed as a degree-two analogue in the broader landscape of ``fake'' surfaces. A new phase began when Borisov and Keum pro duced the first explicit equations for a fake projective plane, opening the door to concrete geometric study of these surfaces. Since then, further ex plicit constructions have been obtained by several authors. In this talk I will survey this development, explain the main ideas behind the passage fro m existence to equations, and discuss possible interactions with fake quadr ics, which may be viewed as a degree-two analogue in the broader landscape of ``fake'' surfaces.

CONTACT:Bojue Wang -Rutgers University DTSTAMP:20260828T001806 DTSTART;TZID=America/New_York:20260429T140000 DTEND;TZID=America/New_York:20260429T150000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR