BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210308T073000Z DTEND:20210308T083000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/1 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bartel (Un iversity of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will be gin by recalling the classical Cohen-Lenstra-Martinet heuristics on the st atistical behaviour of class groups of number fields in families. I will t hen present joint work with Hendrik W. Lenstra Jr. in which we rephrase th e heuristics in terms of Arakelov class groups of number fields\, thereby explaining the otherwise somewhat mysterious looking probability weights i n the original heuristics\; but also disprove the heuristics in two differ ent ways\, and propose corrections.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210315T073000Z DTEND:20210315T083000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/2 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bartel (Un iversity of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will be gin by recalling the classical Cohen-Lenstra-Martinet heuristics on the st atistical behaviour of class groups of number fields in families. I will t hen present joint work with Hendrik W. Lenstra Jr. in which we rephrase th e heuristics in terms of Arakelov class groups of number fields\, thereby explaining the otherwise somewhat mysterious looking probability weights i n the original heuristics\; but also disprove the heuristics in two differ ent ways\, and propose corrections.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210322T073000Z DTEND:20210322T083000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/3 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bartel (Un iversity of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will be gin by recalling the classical Cohen-Lenstra-Martinet heuristics on the st atistical behaviour of class groups of number fields in families. I will t hen present joint work with Hendrik W. Lenstra Jr. in which we rephrase th e heuristics in terms of Arakelov class groups of number fields\, thereby explaining the otherwise somewhat mysterious looking probability weights i n the original heuristics\; but also disprove the heuristics in two differ ent ways\, and propose corrections.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210412T063000Z DTEND:20210412T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/6 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leide n University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic arguments. The y play a central role in CM theory and have close connections with the cla ss field theory of imaginary quadratic fields. With the advent of the work of Gross and Zagier\, investigations of the prime factorisation of differ ences of singular moduli have led to a renaissance of the subject\, and pa ved the way for their celebrated work on Heegner points on elliptic curves . \n\n\nIn this series of talks\, we will explore what happens when we rep lace the imaginary quadratic fields in CM theory with real quadratic field s\, and propose a framework for a conjectural 'RM theory'\, based on the n otion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the wor k of Gross and Zagier\, particularly the analytic arguments based on the d iagonal restrictions of a family of Eisenstein series studied by Hecke in the early 20th century. We will then discuss the theory of RM singular mod uli\, as well as the extent to which arguments based on analytic families of modular forms can be fruitful. In particular\, I will discuss recent pr ogress obtained in various joint works with Henri Darmon and Alice Pozzi.\ n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210419T063000Z DTEND:20210419T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/7 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leide n University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic arguments. The y play a central role in CM theory and have close connections with the cla ss field theory of imaginary quadratic fields. With the advent of the work of Gross and Zagier\, investigations of the prime factorisation of differ ences of singular moduli have led to a renaissance of the subject\, and pa ved the way for their celebrated work on Heegner points on elliptic curves . \n\n\nIn this series of talks\, we will explore what happens when we rep lace the imaginary quadratic fields in CM theory with real quadratic field s\, and propose a framework for a conjectural 'RM theory'\, based on the n otion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the wor k of Gross and Zagier\, particularly the analytic arguments based on the d iagonal restrictions of a family of Eisenstein series studied by Hecke in the early 20th century. We will then discuss the theory of RM singular mod uli\, as well as the extent to which arguments based on analytic families of modular forms can be fruitful. In particular\, I will discuss recent pr ogress obtained in various joint works with Henri Darmon and Alice Pozzi.\ n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210426T063000Z DTEND:20210426T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/8 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leide n University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic arguments. The y play a central role in CM theory and have close connections with the cla ss field theory of imaginary quadratic fields. With the advent of the work of Gross and Zagier\, investigations of the prime factorisation of differ ences of singular moduli have led to a renaissance of the subject\, and pa ved the way for their celebrated work on Heegner points on elliptic curves . \n\n\nIn this series of talks\, we will explore what happens when we rep lace the imaginary quadratic fields in CM theory with real quadratic field s\, and propose a framework for a conjectural 'RM theory'\, based on the n otion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the wor k of Gross and Zagier\, particularly the analytic arguments based on the d iagonal restrictions of a family of Eisenstein series studied by Hecke in the early 20th century. We will then discuss the theory of RM singular mod uli\, as well as the extent to which arguments based on analytic families of modular forms can be fruitful. In particular\, I will discuss recent pr ogress obtained in various joint works with Henri Darmon and Alice Pozzi.\ n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/8/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210503T063000Z DTEND:20210503T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/9 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby David Hansen (Max Planck Institute for Mathematics) as part of Arithmetic Monday\n\n\n Abstract\nLocal Shimura varieties are non-archimedean analytic spaces anal ogous to Shimura varieties\, whose cohomology is expected to realize (in a precise sense) both the local Langlands correspondence and the local Jacq uet-Langlands correspondence. In these lectures\, I'll review the theory o f local Shimura varieties\, and explain what can be proven about their coh omology using current technology. Some of this material is joint work with Tasho Kaletha and Jared Weinstein.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/9/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210510T063000Z DTEND:20210510T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/10 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby David Hanse n (Max Planck Institute for Mathematics) as part of Arithmetic Monday\n\n\ nAbstract\nLocal Shimura varieties are non-archimedean analytic spaces ana logous to Shimura varieties\, whose cohomology is expected to realize (in a precise sense) both the local Langlands correspondence and the local Jac quet-Langlands correspondence. In these lectures\, I'll review the theory of local Shimura varieties\, and explain what can be proven about their co homology using current technology. Some of this material is joint work wit h Tasho Kaletha and Jared Weinstein.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210517T063000Z DTEND:20210517T073000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/11 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby David Hanse n (Max Planck Institute for Mathematics) as part of Arithmetic Monday\n\n\ nAbstract\nLocal Shimura varieties are non-archimedean analytic spaces ana logous to Shimura varieties\, whose cohomology is expected to realize (in a precise sense) both the local Langlands correspondence and the local Jac quet-Langlands correspondence. In these lectures\, I'll review the theory of local Shimura varieties\, and explain what can be proven about their co homology using current technology. Some of this material is joint work wit h Tasho Kaletha and Jared Weinstein.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210524T020000Z DTEND:20210524T033000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/12 DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves\, I\nby Debanjana Kundu (T he University of British Columbia) as part of Arithmetic Monday\n\n\nAbstr act\nTalk 1: Iwasawa Theory: Background\nThe first talk will be introducto ry in nature and the aim will be to make sure that non-experts can follow the remaining of the lecture series. We will start by discussing the notio ns introduced by Iwasawa starting in the late 1950's. We will then describ e the work of Mazur (from 1972) which started the subject of "Iwasawa theo ry of Selmer groups of elliptic curves". We will briefly explain the contr ibutions of Greenberg\, some of which we will return to in the subsequent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of elliptic curv es\nWe will start by introducing the notion of fine Selmer group of an ell iptic curve\, the study of which was initiated by Coates-Sujatha (2005). A s we will see\, these objects are subgroups of Selmer groups which are ver y closely related to class groups. Motivated by conjectures in classical I wasawa theory\, they formulated two conjectures for fine Selmer groups of elliptic curves. I will report on some modest progress I made in this dire ction during my PhD. \n\nTalk 3: Statistics for Iwasawa Invariants\nIn my final talk\, I will discuss some recent results (joint with Anwesh Ray). H ere\, we study the average behaviour of the Iwasawa invariants for the Sel mer groups of elliptic curves\, setting out new directions in arithmetic s tatistics and Iwasawa theory.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210531T020000Z DTEND:20210531T033000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/13 DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves\, II\nby Debanjana Kundu ( The University of British Columbia) as part of Arithmetic Monday\n\n\nAbst ract\nTalk 1: Iwasawa Theory: Background\nThe first talk will be introduct ory in nature and the aim will be to make sure that non-experts can follow the remaining of the lecture series. We will start by discussing the noti ons introduced by Iwasawa starting in the late 1950's. We will then descri be the work of Mazur (from 1972) which started the subject of "Iwasawa the ory of Selmer groups of elliptic curves". We will briefly explain the cont ributions of Greenberg\, some of which we will return to in the subsequent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of elliptic cur ves\nWe will start by introducing the notion of fine Selmer group of an el liptic curve\, the study of which was initiated by Coates-Sujatha (2005). As we will see\, these objects are subgroups of Selmer groups which are ve ry closely related to class groups. Motivated by conjectures in classical Iwasawa theory\, they formulated two conjectures for fine Selmer groups of elliptic curves. I will report on some modest progress I made in this dir ection during my PhD. \n\nTalk 3: Statistics for Iwasawa Invariants\nIn my final talk\, I will discuss some recent results (joint with Anwesh Ray). Here\, we study the average behaviour of the Iwasawa invariants for the Se lmer groups of elliptic curves\, setting out new directions in arithmetic statistics and Iwasawa theory.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210607T020000Z DTEND:20210607T033000Z DTSTAMP:20260422T225705Z UID:ArithmeticMonday/14 DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves\, III\nby Debanjana Kundu (The University of British Columbia) as part of Arithmetic Monday\n\n\nAbs tract\nTalk 1: Iwasawa Theory: Background The first talk will be introduct ory in nature and the aim will be to make sure that non-experts can follow the remaining of the lecture series. We will start by discussing the noti ons introduced by Iwasawa starting in the late 1950's. We will then descri be the work of Mazur (from 1972) which started the subject of "Iwasawa the ory of Selmer groups of elliptic curves". We will briefly explain the cont ributions of Greenberg\, some of which we will return to in the subsequent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of elliptic cur ves We will start by introducing the notion of fine Selmer group of an ell iptic curve\, the study of which was initiated by Coates-Sujatha (2005). A s we will see\, these objects are subgroups of Selmer groups which are ver y closely related to class groups. Motivated by conjectures in classical I wasawa theory\, they formulated two conjectures for fine Selmer groups of elliptic curves. I will report on some modest progress I made in this dire ction during my PhD.\n\nTalk 3: Statistics for Iwasawa Invariants In my fi nal talk\, I will discuss some recent results (joint with Anwesh Ray). Her e\, we study the average behaviour of the Iwasawa invariants for the Selme r groups of elliptic curves\, setting out new directions in arithmetic sta tistics and Iwasawa theory.\n LOCATION:https://researchseminars.org/talk/ArithmeticMonday/14/ END:VEVENT END:VCALENDAR