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:20260404T110652Z UID:ArithmeticMonday/1 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bar tel (University of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will begin by recalling the classical Cohen-Lenstra-Martinet heuristics on the statistical behaviour of class groups of number fields in families. I will then present joint work with Hendrik W. Lenstra Jr. in which we reph rase the heuristics in terms of Arakelov class groups of number fields\, t hereby explaining the otherwise somewhat mysterious looking probability we ights in the original heuristics\; but also disprove the heuristics in two different ways\, and propose corrections.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210315T073000Z DTEND:20210315T083000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/2 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bar tel (University of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will begin by recalling the classical Cohen-Lenstra-Martinet heuristics on the statistical behaviour of class groups of number fields in families. I will then present joint work with Hendrik W. Lenstra Jr. in which we reph rase the heuristics in terms of Arakelov class groups of number fields\, t hereby explaining the otherwise somewhat mysterious looking probability we ights in the original heuristics\; but also disprove the heuristics in two different ways\, and propose corrections.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210322T073000Z DTEND:20210322T083000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/3 DESCRIPTION:Title: On class groups of "random" number fields\nby Alex Bar tel (University of Glasgow) as part of Arithmetic Monday\n\n\nAbstract\nI will begin by recalling the classical Cohen-Lenstra-Martinet heuristics on the statistical behaviour of class groups of number fields in families. I will then present joint work with Hendrik W. Lenstra Jr. in which we reph rase the heuristics in terms of Arakelov class groups of number fields\, t hereby explaining the otherwise somewhat mysterious looking probability we ights in the original heuristics\; but also disprove the heuristics in two different ways\, and propose corrections.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210412T063000Z DTEND:20210412T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/6 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leiden University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic argumen ts. They play a central role in CM theory and have close connections with the class field theory of imaginary quadratic fields. With the advent of t he work of Gross and Zagier\, investigations of the prime factorisation of differences of singular moduli have led to a renaissance of the subject\, and paved 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 replace the imaginary quadratic fields in CM theory with real quadrati c fields\, and propose a framework for a conjectural 'RM theory'\, based o n the notion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the work of Gross and Zagier\, particularly the analytic arguments based o n the diagonal restrictions of a family of Eisenstein series studied by He cke in the early 20th century. We will then discuss the theory of RM singu lar moduli\, as well as the extent to which arguments based on analytic fa milies of modular forms can be fruitful. In particular\, I will discuss re cent progress obtained in various joint works with Henri Darmon and Alice Pozzi.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210419T063000Z DTEND:20210419T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/7 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leiden University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic argumen ts. They play a central role in CM theory and have close connections with the class field theory of imaginary quadratic fields. With the advent of t he work of Gross and Zagier\, investigations of the prime factorisation of differences of singular moduli have led to a renaissance of the subject\, and paved 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 replace the imaginary quadratic fields in CM theory with real quadrati c fields\, and propose a framework for a conjectural 'RM theory'\, based o n the notion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the work of Gross and Zagier\, particularly the analytic arguments based o n the diagonal restrictions of a family of Eisenstein series studied by He cke in the early 20th century. We will then discuss the theory of RM singu lar moduli\, as well as the extent to which arguments based on analytic fa milies of modular forms can be fruitful. In particular\, I will discuss re cent progress obtained in various joint works with Henri Darmon and Alice Pozzi.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vonk (Leiden University) DTSTART:20210426T063000Z DTEND:20210426T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/8 DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (Leiden University) as part of Arithmetic Monday\n\n\nAbstract\nSingular moduli are special values of the j-function at imaginary quadratic argumen ts. They play a central role in CM theory and have close connections with the class field theory of imaginary quadratic fields. With the advent of t he work of Gross and Zagier\, investigations of the prime factorisation of differences of singular moduli have led to a renaissance of the subject\, and paved 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 replace the imaginary quadratic fields in CM theory with real quadrati c fields\, and propose a framework for a conjectural 'RM theory'\, based o n the notion of rigid meromorphic cocycles\, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the work of Gross and Zagier\, particularly the analytic arguments based o n the diagonal restrictions of a family of Eisenstein series studied by He cke in the early 20th century. We will then discuss the theory of RM singu lar moduli\, as well as the extent to which arguments based on analytic fa milies of modular forms can be fruitful. In particular\, I will discuss re cent progress obtained in various joint works with Henri Darmon and Alice Pozzi.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/8/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210503T063000Z DTEND:20210503T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/9 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby David Hansen (Max Planck Institute for Mathematics) as part of Arithmetic Monda y\n\n\nAbstract\nLocal Shimura varieties are non-archimedean analytic spac es analogous to Shimura varieties\, whose cohomology is expected to realiz e (in a precise sense) both the local Langlands correspondence and the loc al Jacquet-Langlands correspondence. In these lectures\, I'll review the t heory of local Shimura varieties\, and explain what can be proven about th eir cohomology using current technology. Some of this material is joint wo rk with Tasho Kaletha and Jared Weinstein.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/9/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210510T063000Z DTEND:20210510T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/10 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby Davi d Hansen (Max Planck Institute for Mathematics) as part of Arithmetic Mond ay\n\n\nAbstract\nLocal Shimura varieties are non-archimedean analytic spa ces analogous to Shimura varieties\, whose cohomology is expected to reali ze (in a precise sense) both the local Langlands correspondence and the lo cal Jacquet-Langlands correspondence. In these lectures\, I'll review the theory of local Shimura varieties\, and explain what can be proven about t heir cohomology using current technology. Some of this material is joint w ork with Tasho Kaletha and Jared Weinstein.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hansen (Max Planck Institute for Mathematics) DTSTART:20210517T063000Z DTEND:20210517T073000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/11 DESCRIPTION:Title: Local Shimura varieties and their cohomology\nby Davi d Hansen (Max Planck Institute for Mathematics) as part of Arithmetic Mond ay\n\n\nAbstract\nLocal Shimura varieties are non-archimedean analytic spa ces analogous to Shimura varieties\, whose cohomology is expected to reali ze (in a precise sense) both the local Langlands correspondence and the lo cal Jacquet-Langlands correspondence. In these lectures\, I'll review the theory of local Shimura varieties\, and explain what can be proven about t heir cohomology using current technology. Some of this material is joint w ork with Tasho Kaletha and Jared Weinstein.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210524T020000Z DTEND:20210524T033000Z DTSTAMP:20260404T110652Z UID:ArithmeticMonday/12 DESCRIPTION:Title: Iwasawa Theory of Elliptic Curves\, I\nby Debanjana K undu (The University of British Columbia) as part of Arithmetic Monday\n\n \nAbstract\nTalk 1: Iwasawa Theory: Background\nThe first talk will be int roductory 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 th e notions introduced by Iwasawa starting in the late 1950's. We will then describe the work of Mazur (from 1972) which started the subject of "Iwasa wa theory of Selmer groups of elliptic curves". We will briefly explain th e contributions of Greenberg\, some of which we will return to in the subs equent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of ellipt ic curves\nWe will start by introducing the notion of fine Selmer group of an elliptic curve\, the study of which was initiated by Coates-Sujatha (2 005). As we will see\, these objects are subgroups of Selmer groups which are very closely related to class groups. Motivated by conjectures in clas sical Iwasawa theory\, they formulated two conjectures for fine Selmer gro ups of elliptic curves. I will report on some modest progress I made in th is direction 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 Selmer groups of elliptic curves\, setting out new directions in arith metic statistics and Iwasawa theory.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210531T020000Z DTEND:20210531T033000Z DTSTAMP:20260404T110652Z 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\nAbstract\nTalk 1: Iwasawa Theory: Background\nThe first talk will be in troductory 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 t he notions introduced by Iwasawa starting in the late 1950's. We will then describe the work of Mazur (from 1972) which started the subject of "Iwas awa theory of Selmer groups of elliptic curves". We will briefly explain t he contributions of Greenberg\, some of which we will return to in the sub sequent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of ellip tic curves\nWe will start by introducing the notion of fine Selmer group o f an elliptic curve\, the study of which was initiated by Coates-Sujatha ( 2005). As we will see\, these objects are subgroups of Selmer groups which are very closely related to class groups. Motivated by conjectures in cla ssical Iwasawa theory\, they formulated two conjectures for fine Selmer gr oups of elliptic curves. I will report on some modest progress I made in t his direction 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 Selmer groups of elliptic curves\, setting out new directions in arit hmetic statistics and Iwasawa theory.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Debanjana Kundu (The University of British Columbia) DTSTART:20210607T020000Z DTEND:20210607T033000Z DTSTAMP:20260404T110652Z 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\nAbstract\nTalk 1: Iwasawa Theory: Background The first talk will be in troductory 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 t he notions introduced by Iwasawa starting in the late 1950's. We will then describe the work of Mazur (from 1972) which started the subject of "Iwas awa theory of Selmer groups of elliptic curves". We will briefly explain t he contributions of Greenberg\, some of which we will return to in the sub sequent lectures.\n\nTalk 2: Iwasawa Theory of Fine Selmer Groups of ellip tic curves We will start by introducing the notion of fine Selmer group of an elliptic curve\, the study of which was initiated by Coates-Sujatha (2 005). As we will see\, these objects are subgroups of Selmer groups which are very closely related to class groups. Motivated by conjectures in clas sical Iwasawa theory\, they formulated two conjectures for fine Selmer gro ups of elliptic curves. I will report on some modest progress I made in th is direction during my PhD.\n\nTalk 3: Statistics for Iwasawa Invariants I n my final talk\, I will discuss some recent results (joint with Anwesh Ra y). Here\, we study the average behaviour of the Iwasawa invariants for th e Selmer groups of elliptic curves\, setting out new directions in arithme tic statistics and Iwasawa theory.\n LOCATION:https://stable.researchseminars.org/talk/ArithmeticMonday/14/ END:VEVENT END:VCALENDAR