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DTSTART;TZID=Europe/Berlin:20220718T121500
DTEND;TZID=Europe/Berlin:20220718T144500
DTSTAMP:20260417T044330
CREATED:20220701T110952Z
LAST-MODIFIED:20220704T090227Z
UID:3239-1658146500-1658155500@crc326gaus.de
SUMMARY:Lecture Series "Some recent developments in singularity theory in mixed and positive characteristic algebraic geometry"
DESCRIPTION:There will be a 4-talk Lecture series on mixed characteristic algebraic geometry by Kevin Tucker (UIC) during July here in Mainz. The first talk is a Kolloquium style talk and should be interesting for (und largely understandable by) most people; and you can decide if you continue with the other 3\, more demanding (but even more rewarding)\, talks. \nTalk 1: Wednesday July 13: 12:15–13:45\nTalk 2: Monday July 18: 12:15–14:45\nTalk 3: Monday July 18: 16:15–17:45\nTalk 4: Wednesday July 20: 12:15-13:35 \nAll talks are taking place in the Hilbertraum 05-432\, Staudingerweg 9\, 55099 Mainz\, or alternatively via Zoom:\nhttps://zoom.us/j/91070632898?pwd=ODM2a1RlZ1RwdVhxVkg2dEk1Vy9CZz09 Meeting ID: 910 7063 2898 Passcode: 123123 \nTitle: Some recent developments in singularity theory in mixed and positive characteristic algebraic geometry\nSpeaker: Kevin Tucker (University of Illinois at Chicago)\nAbstract: Standard “reduction to characteristic p” techniques have long been used to relate singularities defined via the Frobenius map in positive characteristic and those arising in complex algebraic geometry and the Minimal Model Program (MMP). For example\, log terminal and F-regular singularities are known to correspond to one another via reduction to characteristic p >> 0. Exciting developments have recently made it possible to exploit these connections in the mixed characteristic setting as well\, drawing on the (conjectured) characterization of F-regular rings as splinters in positive characteristic. A ring is a splinter if it is a direct summand of every finite cover\, and Hochster’s direct summand conjecture (now a Theorem) is the modest assertion that a regular ring of any characteristic is a splinter. This conjecture was settled affirmatively by André in 2018 who proved the mixed characteristic case more than three decades after Hochster’s verification of the conjecture in equal characteristic using Frobenius techniques. In these talks\, I will discuss some recent works on splinter rings in mixed and positive characteristics. In particular\, inspired by the result of Bhatt in 2020 on the Cohen-Macaulayness of the absolute integral closure\, I will describe a global notion of splinter in the mixed characteristic setting called global +-regularity with applications to birational geometry in mixed characteristic. This can be seen as a generalization of the theory of globally F-regular pairs from positive to mixed characteristic\, and led to the successful development of the three dimensional MMP in mixed characteristics (0; p > 5).
URL:https://crc326gaus.de/event/lecture-series-on-mixed-characteristic-birational-geometry-2/
LOCATION:Mainz\, Hilbertraum (05-432) and Zoom
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20220713T121500
DTEND;TZID=Europe/Berlin:20220713T134500
DTSTAMP:20260417T044330
CREATED:20220701T110741Z
LAST-MODIFIED:20220704T090127Z
UID:3237-1657714500-1657719900@crc326gaus.de
SUMMARY:Lecture Series "Some recent developments in singularity theory in mixed and positive characteristic algebraic geometry"
DESCRIPTION:There will be a 4-talk Lecture series on mixed characteristic algebraic geometry by Kevin Tucker (UIC) during July here in Mainz. The first talk is a Kolloquium style talk and should be interesting for (und largely understandable by) most people; and you can decide if you continue with the other 3\, more demanding (but even more rewarding)\, talks. \nTalk 1: Wednesday July 13: 12:15–13:45\nTalk 2: Monday July 18: 12:15–14:45\nTalk 3: Monday July 18: 16:15–17:45\nTalk 4: Wednesday July 20: 12:15-13:35 \nAll talks are taking place in the Hilbertraum 05-432\, Staudingerweg 9\, 55099 Mainz\, or alternatively via Zoom:\nhttps://zoom.us/j/91070632898?pwd=ODM2a1RlZ1RwdVhxVkg2dEk1Vy9CZz09 Meeting ID: 910 7063 2898 Passcode: 123123 \nTitle: Some recent developments in singularity theory in mixed and positive characteristic algebraic geometry\nSpeaker: Kevin Tucker (University of Illinois at Chicago)\nAbstract: Standard “reduction to characteristic p” techniques have long been used to relate singularities defined via the Frobenius map in positive characteristic and those arising in complex algebraic geometry and the Minimal Model Program (MMP). For example\, log terminal and F-regular singularities are known to correspond to one another via reduction to characteristic p >> 0. Exciting developments have recently made it possible to exploit these connections in the mixed characteristic setting as well\, drawing on the (conjectured) characterization of F-regular rings as splinters in positive characteristic. A ring is a splinter if it is a direct summand of every finite cover\, and Hochster’s direct summand conjecture (now a Theorem) is the modest assertion that a regular ring of any characteristic is a splinter. This conjecture was settled affirmatively by André in 2018 who proved the mixed characteristic case more than three decades after Hochster’s verification of the conjecture in equal characteristic using Frobenius techniques. In these talks\, I will discuss some recent works on splinter rings in mixed and positive characteristics. In particular\, inspired by the result of Bhatt in 2020 on the Cohen-Macaulayness of the absolute integral closure\, I will describe a global notion of splinter in the mixed characteristic setting called global +-regularity with applications to birational geometry in mixed characteristic. This can be seen as a generalization of the theory of globally F-regular pairs from positive to mixed characteristic\, and led to the successful development of the three dimensional MMP in mixed characteristics (0; p > 5).
URL:https://crc326gaus.de/event/lecture-series-on-mixed-characteristic-birational-geometry/
LOCATION:Mainz\, Hilbertraum (05-432) and Zoom
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20220707T171500
DTEND;TZID=Europe/Berlin:20220707T183000
DTSTAMP:20260417T044330
CREATED:20220609T081436Z
LAST-MODIFIED:20220707T120136Z
UID:3106-1657214100-1657218600@crc326gaus.de
SUMMARY:Modularity of Galois representations\, from Ramanujan to Serre's Conjecture
DESCRIPTION:CRC Colloquium\n9. Emil Artin Lecture \nProf. Dr. Chandrashekhar Khare\, Department of Mathematics\, UCLA \nRamanujan made a series of conjectures in his 1916 paper “On some arithmetical functions’’ on what is now called the Ramanujan $\tau$ function.  Part of these conjectures were proved soon after Ramanujan formulated them by Mordell\, while one of his conjectures (which is now the first of a vast web of conjectures in the theory of automorphic forms)  took almost 6 decades to be settled (in work of Deligne). A  congruence Ramanujan observed for $\tau(n)$ modulo 691 in the same paper\,  led to Serre and Swinnerton-Dyer developing a geometric theory of mod $p$ modular forms to explain some of Ramanujan’s observations. It was in the context of the theory of mod $p$ modular forms that Serre made his modularity conjecture\, which was initially formulated in a letter of Serre to Tate in 1973.\nI will narrate  this story\, starting from Ramanujan’s work  in 1916\, to the formulation of Serre’s conjecture in 1973\,  to its resolution  in 2009 by Jean-Pierre Wintenberger and myself (using as a key ingredient the modularity lifting method developed by Wiles in his proof of Fermat’s Last Theorem). I will also try to indicate why this subject is very much alive and in spite of all the  progress still in its infancy.
URL:https://crc326gaus.de/event/modularity-of-galois-representations-from-ramanujan-to-serres-conjecture/
LOCATION:Heidelberg\, MATHEMATIKON\, Hörsaal
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20220428T090000
DTEND;TZID=Europe/Berlin:20220428T094500
DTSTAMP:20260417T044330
CREATED:20220303T124159Z
LAST-MODIFIED:20220303T151115Z
UID:2356-1651136400-1651139100@crc326gaus.de
SUMMARY:To infinity and beyond
DESCRIPTION:Judith Ludwig (Universität Heidelberg) \nThe introductory lecture from research will be given by Dr. Judith Ludwig on ‘Girls’Day 2022 – MINTmachen!’ at Heidelberg University.
URL:https://crc326gaus.de/event/to-infinity-and-much-further/
LOCATION:Heidelberg on ‘Girls’Day 2022 – MINTmachen!
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210927
DTEND;VALUE=DATE:20211009
DTSTAMP:20260417T044330
CREATED:20210728T154641Z
LAST-MODIFIED:20210914T225958Z
UID:1191-1632700800-1633737599@crc326gaus.de
SUMMARY:Workshop Linear Algebraic Groups
DESCRIPTION:
URL:https://crc326gaus.de/event/workshop-linear-algebraic-groups/
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210921
DTEND;VALUE=DATE:20210925
DTSTAMP:20260417T044330
CREATED:20210915T143704Z
LAST-MODIFIED:20210915T143704Z
UID:1407-1632182400-1632527999@crc326gaus.de
SUMMARY:Conference on vertex algebras and related topics
DESCRIPTION:In this conference we want to bring together people from different directions in the theory of vertex algebras and from related areas to discuss recent advances.
URL:https://crc326gaus.de/event/conference-on-vertex-algebras-and-related-topics/
LOCATION:Darmstadt and Zoom
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20210713T150000
DTEND;TZID=Europe/Berlin:20210715T170000
DTSTAMP:20260417T044330
CREATED:20210914T235134Z
LAST-MODIFIED:20210914T235357Z
UID:1346-1626188400-1626368400@crc326gaus.de
SUMMARY:Ruth Moufang Lectures 2021
DESCRIPTION:This year’s speaker will be Jennifer Balakrishnan with three lectures on rational points on curves. The event will be opened by Andrea Blunck with a lecture on the life and work of Ruth Moufang.
URL:https://crc326gaus.de/event/ruth-moufang-lectures-2021/
LOCATION:Zoom
CATEGORIES:GAUS-Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20210709T160000
DTEND;TZID=Europe/Berlin:20210709T174500
DTSTAMP:20260417T044330
CREATED:20210915T000949Z
LAST-MODIFIED:20210915T011602Z
UID:1349-1625846400-1625852700@crc326gaus.de
SUMMARY:Pre-Seminar for the Ruth Moufang Lectures
DESCRIPTION:In the very first instalment of the Ruth Moufang Lectures\, Jennifer Balakrishnan will talk about rational points on curves. In the tradition of the “Gingko-Seminar”\, we offer a “pre-seminar” as preparation consisting of  two 45 minute talks. The pre-seminar is aimed at PhD students and PostDocs\, as well as interested Bachelor and Master students.\n \n1. What is… a p-adic number? (Theresa Kumpitsch) \nThe p-adic numbers were invented (or discovered depending on your philosophy) at the beginning of the twentieth century by Kurt Hensel following the observation that that numbers behave similar to functions in many ways. In this short introduction to p-adic numbers we want to explore this analogy\, learn about different ways of expressing p-adic numbers\, look at lots of examples and get a sense of why they play a role in the theory of Diophantine equations. \n2. What is… an algebraic curve? (Martin Lüdtke) \nRoughly\, an algebraic curve is a 1-dimensional shape defined by polynomial equations. Examples are parabolas\, hyperbolas\, elliptic curves\, or the Fermat curves defined by x^n + y^n = z^n. We want to explore first the geometry of curves and discover the genus as a discrete invariant. We then turn to the problem of finding rational solutions to equations in two variables. We discuss several examples and see how the set of rational solutions is governed by the geometry of the associated algebraic curve. \nZoom coordinates: \nhttps://uni-frankfurt.zoom.us/j/92910007294?pwd=MTFwU2VKR3MvU1JWanZIUDlmYms4UT09  Meeting ID: 929 1000 7294Passcode: 931095
URL:https://crc326gaus.de/event/pre-seminar-for-the-ruth-moufang-lectures/
LOCATION:Zoom
CATEGORIES:GAUS-Event
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