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:20210201T153000 RDATE:20210314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20211107T010000 RDATE:20220313T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20221106T010000 RDATE:20230312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD 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:20210314T030000 RDATE:20211107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20220313T030000 RDATE:20221106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20230312T030000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 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:6ca9128af9cc85fcc4380f7747613332 CATEGORIES:Colloquia CREATED:20220124T095057 SUMMARY:An arithmetic count of rational plane curves LOCATION:Zoom DESCRIPTION:Abstract: There is a unique line through 2 points in the plane, and a uniqu e conic through 5. These counts generalize to a count of degree d rational curves in the plane passing through 3d-1 points. Surprisingly, the problem of determining these numbers is connected to string theory, and it was not until the 1990's that Kontsevich determined them with a recursive formula. Such formulas are valid when you allow your curves to be defined with compl ex coefficients. Over the real numbers, one can obtain a fixed number by we ighting real rational curves by their Welschinger invariant, and work of So lomon provides a recursive formula. It is a feature of A1-homotopy theory t hat analogous real and complex results can indicate the presence of a commo n generalization, valid over a general field. For fields of characteristic not 2 or 3, we give such a generalization. The resulting count is (the stab le isomorphism class) of a bilinear form, or an element of the group comple tion GW(k) of symmetric, non-degenerate, bilinear forms over k. For example , there are 2(<1>+<-1>) + 6<1> + <2>+<2D> rat ional degree 3-plane curves passing through a general configuration of 6 k- points and a pair of conjugate k(sort{D}) points in the plane. No knowledge of A1-homoltopy theory or GW is assumed. This is joint work with Jesse Kas s, Marc Levine, and Jake Solomon.\n X-ALT-DESC;FMTTYPE=text/html:

Abstract: There is a unique line through 2 points in the plane, and a un ique conic through 5. These counts generalize to a count of degree d ration al curves in the plane passing through 3d-1 points. Surprisingly, the probl em of determining these numbers is connected to string theory, and it was n ot until the 1990's that Kontsevich determined them with a recursive formul a. Such formulas are valid when you allow your curves to be defined with co mplex coefficients. Over the real numbers, one can obtain a fixed number by weighting real rational curves by their Welschinger invariant, and work of Solomon provides a recursive formula. It is a feature of A1-homotopy theor y that analogous real and complex results can indicate the presence of a co mmon generalization, valid over a general field. For fields of characterist ic not 2 or 3, we give such a generalization. The resulting count is (the s table isomorphism class) of a bilinear form, or an element of the group com pletion GW(k) of symmetric, non-degenerate, bilinear forms over k. For exam ple, there are 2(<1>+<-1>) + 6<1> + <2>+<2D> rational degree 3-plane curves passing through a general configuration of 6 k-points and a pair of conjugate k(sort{D}) points in the plane. No knowle dge of A1-homoltopy theory or GW is assumed. This is joint work with Jesse Kass, Marc Levine, and Jake Solomon.

CONTACT:Kirsten Wickelgren - Duke University DTSTAMP:20260831T053741 DTSTART;TZID=America/New_York:20220202T153000 DTEND;TZID=America/New_York:20220202T163000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR