BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ramin Takloo-Bighash (Department of Math\, Stat\, and Computer Sci ence\, UIC Chicago\, IL) DTSTART:20210928T150000Z DTEND:20210928T170000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/1 DESCRIPTION:Title: The distribution of rational points on some spherical varieties.\nby R amin Takloo-Bighash (Department of Math\, Stat\, and Computer Science\, UI C Chicago\, IL) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac t\nIn this talk I will discuss a work in progress in which\, together with Sho Tanimoto and Yuri Tschinkel\, we study the distribution of rational p oints on some anisotropic spherical varieties of rank 1 over an arbitrary number field. Our work is the non-split analogue of the results of Valenti n Blomer\, Jörg Brüdern\, Ulrich Derenthal\, and Giuliano Gagliardi wher e they consider split spherical varieties of rank 1 over the rational numb ers\, though our methods are completely different. In our proof we use the theory of automorphic forms\, especially Waldspurger's celebrated theorem on toric periods\, to analyse the height zeta function. Once this analysi s is done\, the result on the distribution of rational points follows from a standard Tauberian theorem. We hope to address split spherical varietie s of rank 1 over an arbitrary number field using similar methods in a futu re work.\n\nMeeting ID: 908 611 6889\nPasscode: ''the order of the symmetr ic group on 9 elements (type the 6-digit number)''\n LOCATION:https://researchseminars.org/talk/FGC-IPM/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Kisin (Harvard University) DTSTART:20211012T140000Z DTEND:20211012T160000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/2 DESCRIPTION:Title: Essential dimension via prismatic cohomology\nby Mark Kisin (Harvard U niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nLe t $f:Y \\rightarrow X$ be a finite covering map of complex algebraic varie ties. The essential dimension of $f$ is the smallest integer $e$ such that \, birationally\, $f$ arises as the pullback of a covering $Y'\\rightarrow X'$ of dimension $e$\, via a map $X \\rightarrow X'$. This invariant goes back to classical questions about reducing the number of parameters in a solution to a general $n$-th degree polynomial\, and appeared in work of K ronecker and Klein on solutions of the quintic. \n\nI will report on joint work with Benson Farb and Jesse Wolfson\, where we introduce a new techni que\, using prismatic cohomology\, to obtain lower bounds on the essential dimension of certain coverings. For example\, we show that for an abelian variety $A$ of dimension $g$ the multiplication by $p$ map $A \\rightarr ow A$ has essential dimension $g$ for almost all primes $p$.\n\nMeeting ID : 908 611 6889 \,\nPasscode: order of the symmetric group on 9 letters (ty pe the 6-digit number)\n LOCATION:https://researchseminars.org/talk/FGC-IPM/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Reza Taleb (Shahid Beheshti University) DTSTART:20211026T140000Z DTEND:20211026T160000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/3 DESCRIPTION:Title: The Coates-Sinnott Conjecture\nby Reza Taleb (Shahid Beheshti Universi ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe Coate s-Sinnott Conjecture was formulated in 1974 as a K-theory analogue of Stic kelberger's Theorem. For a finite abelian extension $E/F$ of number fields and any integer $n\\geq 2$\, this conjecture constructs an element in ter ms of special values of the (equivariant) L-function of $E/F$ at $1-n$ to annihilate the even Quillen K-group $K_{2n-2}(O_E)$ of associated ring of integers $O_E$ over the group ring $\\mathbb{Z}[Gal(E/F)]$. In this talk a fter describing the precise formulation of the conjecture we present the r ecent results. Part of this is a joint work with Manfred Kolster.\n\nMeet ing ID: 908 611 6889 \,\nPasscode: Order of the symmetric group on 9 lette rs (Type the 6-digit number)\n LOCATION:https://researchseminars.org/talk/FGC-IPM/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Shabnam Akhatri (University of Oregon) DTSTART:20211109T140000Z DTEND:20211109T160000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/4 DESCRIPTION:Title: Monogenic cubic rings and Thue equations\nby Shabnam Akhatri (Universi ty of Oregon) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\ nLet K be a cubic number field. We give an absolute upper bound for the nu mber of monogenic orders which have small index (compared to the discrimin ant of K) in the ring of integers of K. This is done by counting the numb er of integral solutions of some cubic Thue equations. This reduction to t he resolution of Thue equations will also allow us to count the number of monogenic orders with a fixed index in the ring of integers of K.\n\nMeeti ng ID: 908 611 6889\, \nPasscode: The order of the symmetric group on 9 el ements (Type the 6-digit number)\n LOCATION:https://researchseminars.org/talk/FGC-IPM/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ali Mohammadi (IPM) DTSTART:20211123T113000Z DTEND:20211123T133000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/5 DESCRIPTION:Title: Bounds on point-conic incidences over finite fields and applications\n by Ali Mohammadi (IPM) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n Abstract\nI will begin with a brief overview of some well-known results in incidence geometry and go on to discuss a recent joint work with Thang Ph am and Audie Warren\, in which we prove upper bounds on the number of inci dences between sets of points and conics over finite fields. I will conclu de the talk by considering applications to certain finite field variants o f Erd\\H{o}s type problems on the number of distinct algebraic distances f ormed by point sets\, including improvements to results of Koh and Sun (20 14) and Shparlinski (2006).\n\nMeeting ID: 908 611 6889\,\nPasscode: The o rder of the symmetric group on 9 elements (Type the 6-digit number)\n LOCATION:https://researchseminars.org/talk/FGC-IPM/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Dabrowski (University of Szczecin) DTSTART:20211207T113000Z DTEND:20211207T133000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/6 DESCRIPTION:Title: On a class of generalized Fermat equations of signature $(2\,2n\,3)$\n by Andrzej Dabrowski (University of Szczecin) as part of FGC-HRI-IPM Numbe r Theory Webinars\n\n\nAbstract\nWe will discuss the generalized Fermat eq uations\n$Ax^2 + By^{2n} = 4z^3$\, assuming (for simplicity) that\nthe cl ass number of the imaginary quadratic field\n$\\mathbb Q(\\sqrt{-AB})$ is one. The methods use techniques\ncoming from Galois representations and mo dular forms\; for\nsmall $n$'s one needs Chabauty type methods. Our result s\,\nconjectures (and methods) extend those given by Bruin\, Chen\net al. in the case $x^2 + y^{2n} = z^3$. This is a joint work\nwith K. Chałupka and G. Soydan.\n\nMeeting ID: 989 8485 8471\, \nPasscode: 039129\n LOCATION:https://researchseminars.org/talk/FGC-IPM/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Amir Ghadermarzi (University of Tehran) DTSTART:20211221T140000Z DTEND:20211221T160000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/7 DESCRIPTION:Title: Integral points on Mordell curves of rank 1\nby Amir Ghadermarzi (Univ ersity of Tehran) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr act\nA well-known theorem of Siegel states that any elliptic curve $E/\\ma thbb{Q}$ has only finitely many integral points. Lang conjectured that the number of integral points on a quasi-minimal model of an elliptic curve s hould be bounded solely in terms of the rank of the group of rational poin ts. Silverman proved Lang's conjecture for the curves with at most a fixed number of primes dividing the denominator of the $j$-invariant. Using mor e explicit methods\, Silverman and Gross compute the dependence of the bou nds on the various constants. In the case of curves of rank 1\, techniques of Ingram on multiples of integral points enable one to prove much better bounds for special families of elliptic curves. In this talk\, we investi gate the integral points on Mordell curves of rank 1.\n\nMeeting ID: 908 6 11 6889\, \nPasscode: the order of the symmetric group on 9 letters (Type the 6-digit number).\n LOCATION:https://researchseminars.org/talk/FGC-IPM/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatma Cicek (IITGandhinagar) DTSTART:20210104T113000Z DTEND:20210104T133000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/8 DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IITGandhinagar) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatma Cicek (IIT Gandhinagar) DTSTART:20210104T113000Z DTEND:20210104T133000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/9 DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhinagar) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatma Cicek (IIT Gandhinagar) DTSTART:20220104T113000Z DTEND:20220104T133000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/10 DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhinagar) a s part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\n‎Selberg's c entral limit theorem is an influential probabilistic result in analytic nu mber theory which roughly states that the logarithm of the Riemann zeta-fu nction $\\zeta(s)$ on the half-line‎\, ‎that is $\\Re s = \\frac12$‎ \, ‎has an approximate two-dimensional Gaussian distribution as $\\Im s \\to \\infty$‎. ‎We will carefully review the important ideas in the p roof of Selberg's theorem and then will mention some variants of it‎. ‎Towards the end of the talk‎\, ‎we will also see some of its applic ations‎.\n\nMeeting ID: 922 2650 4686 \; Passcode: 645549\n LOCATION:https://researchseminars.org/talk/FGC-IPM/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristian David Gonzalez Aviles (Universidad de La Serena) DTSTART:20220201T130000Z DTEND:20220201T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/11 DESCRIPTION:Title: Totally singular algebraic groups\nby Cristian David Gonzalez Aviles (Universidad de La Serena) as part of FGC-HRI-IPM Number Theory Webinars\n \n\nAbstract\nI will define the groups of the title and discuss some examp les.\nWhen they are of positive dimension\, these groups exist only\nover an imperfect field. We will see examples in dimension 1 related to the\npu rely inseparable forms of the additive group\nstudied by Russell in 1970. We will also see some examples of arbitrarily\nhigh dimensions. I hope to convince the audience that this class of\nalgebraic groups is both interes ting and quite large!\n\nMeeting ID: 908 611 6889\,\n\nPasscode: The order of the symmetric group over nine letters (Please type the 6-digit number) .\n LOCATION:https://researchseminars.org/talk/FGC-IPM/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20200315T130000Z DTEND:20200315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/12 DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu mber Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20200315T130000Z DTEND:20200315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/13 DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu mber Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20200315T130000Z DTEND:20200315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/14 DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu mber Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20200315T130000Z DTEND:20200315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/15 DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu mber Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20200315T130000Z DTEND:20200315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/16 DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu mber Theory Webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/FGC-IPM/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Semih Ozlem (Yeditepe University) DTSTART:20220315T130000Z DTEND:20220315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/17 DESCRIPTION:Title: On the motivic Galois group of a number field\nby Semih Ozlem (Yedite pe University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract \nAim of this talk is to briefly introduce the motivic Galois group and st ate a potential answer to Langlands' conjecture regarding the relation of Langlands' group and motivic Galois group.\n\nMeeting ID: 908 611 6889\;\n Passcode: the order of the symmetric group on 9 letters (please type the 6 -digit number)\n LOCATION:https://researchseminars.org/talk/FGC-IPM/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Farzad Aryan (Göttingen University) DTSTART:20220405T120000Z DTEND:20220405T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/18 DESCRIPTION:Title: On the Riemann Zeta Function\nby Farzad Aryan (Göttingen University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will discu ss the Riemann zeta function and the significance of its zeros to prime nu mbers. Also\, I will look at the distribution of zeta zeros and mention so me of my related works on the subject.\n\nJoin Zoom Meeting\nhttps://us06w eb.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting I D: 872 1214 6791\nPasscode: 362880\n LOCATION:https://researchseminars.org/talk/FGC-IPM/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Chirantan Chowdhury (University of Duisburg-Essen) DTSTART:20220419T120000Z DTEND:20220419T130000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/19 DESCRIPTION:Title: Motivic Homotopy Theory of Algebraic Stacks\nby Chirantan Chowdhury ( University of Duisburg-Essen) as part of FGC-HRI-IPM Number Theory Webinar s\n\nAbstract: TBA\n\nZoom link:\nhttps://us06web.zoom.us/j/87212146791?pw d=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPasscode: 362880\n LOCATION:https://researchseminars.org/talk/FGC-IPM/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Hamza Yesilyurt (Bilkent University) DTSTART:20220517T120000Z DTEND:20220517T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/20 DESCRIPTION:Title: A Modular Equation of Degree 61\nby Hamza Yesilyurt (Bilkent Universi ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nA modular equation of degree $n$ is an equation that relates classical theta functi ons with arguments $q$ and $q^n$. The theory of modular equations started with the works of Landen\, Jacobi and Legendre. The theory gained populari ty again with enormous contributions made by Ramanujan. In this talk we wi ll give a brief introduction to the theory of modular equations and then o btain a new modular equation of degree $61$ by using a generalization of a theta function identity due to David M. Bressoud. This is a joint work with Ahmet Güloğlu.\n\nJoin Zoom Meeting:\nhttps://us06web.zoom.us/j/872 12146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791 \nPasscode: 362880\n LOCATION:https://researchseminars.org/talk/FGC-IPM/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Somnath Jha (IIT Kanpur) DTSTART:20220531T120000Z DTEND:20220531T130000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/21 DESCRIPTION:Title: Fine Selmer group of elliptic curves over global fields\nby Somnath J ha (IIT Kanpur) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac t\nThe (p-infinity) fine Selmer group (also called the 0-Selmer group) of an elliptic curve is a subgroup of the usual p-infinity Selmer group of an elliptic curve and is related to the first and the second Iwasawa cohomol ogy groups. Coates-Sujatha observed that the structure of the fine Selmer group over the cyclotomic Z_p extension of a number field K is intricately related to Iwasawa's \\mu-invariant vanishing conjecture on the growth of p-part of the ideal class group of K in the cyclotomic tower. In this tal k\, we will discuss the structure and properties of the fine Selmer group over certain p-adic Lie extensions of global fields. This talk is based on joint work with Sohan Ghosh and Sudhanshu Shekhar.\n\nZoom link:\nhttps: //us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMe eting ID: 872 1214 6791\nPasscode: 362880\n LOCATION:https://researchseminars.org/talk/FGC-IPM/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Abbas Maarefparvar (Institute for Research in Fundamental Sciences (IPM)) DTSTART:20220614T120000Z DTEND:20220614T130000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/22 DESCRIPTION:Title: On BRZ exact sequence for finite Galois extensions of number fields\n by Abbas Maarefparvar (Institute for Research in Fundamental Sciences (IPM )) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this ta lk\, I will shortly explain how to use some cohomological results of Brume r-Rosen and Zantema to obtain a four-term exact sequence\, called ``BRZ’ ’ standing for these authors\, which reveals some information about str ongly ambiguous ideal classes (coinciding with relative Polya group) of a finite Galois extension of number fields. As an application of the BRZ\, I will reprove some well known results in the literature. Then\, as a minor modification on relative Polya group for a finite extension of number fie lds\, I will introduce the notion of ``relative Ostrowski quotient'' and give some new approaches of the BRZ exact sequence. The main part of my t alk is concerning a joint work with Ali Rajaei and Ehsan Shahoseini.\n\nZo om link:\nhttps://us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbk lEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPasscode: 362880\n LOCATION:https://researchseminars.org/talk/FGC-IPM/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohammad Sadek DTSTART:20221024T130000Z DTEND:20221024T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/23 DESCRIPTION:Title: How often do polynomials hit squares?\nby Mohammad Sadek as part of F GC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGiven a polynomial with r ational coefficients\, one may investigate the possible values that may be attained by these polynomials over the set of rational numbers. For centu ries\, number theorists have been giving due attention to square rational values assumed by rational polynomials. It turns out that seeking an answe r to this question connects number theory and geometry. Answering this que stion for a polynomial in one variable will lead us to study the arithmeti c of certain algebraic curves. We will spend some time explaining the geom etry beneath the question when the degree of the polynomial is at least 3. For polynomials in more than one variable\, the geometric structure is re mote. In the latter case\, we will present some of the old and recent deve lopments in the theory shedding some light on some classical Diophantine q uestions.\n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID: 856 1386 0958\n LOCATION:https://researchseminars.org/talk/FGC-IPM/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Haydar Goral DTSTART:20221107T130000Z DTEND:20221107T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/24 DESCRIPTION:Title: Lehmer’s conjecture via model theory\nby Haydar Goral as part of FG C-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we first in troduce the height function and the Mahler measure on the field of algebra ic numbers. We state and give a survey on Lehmer’s conjecture for the Ma hler measure\, which is still an open problem. Then\, we consider the fiel d of algebraic numbers with elements of small Mahler measures in terms of model theory\, and we link this theory with Lehmer’s conjecture. Our ap proach is based on Van der Waerden's theorem from additive combinatorics.\ n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID: 856 1386 0958\n LOCATION:https://researchseminars.org/talk/FGC-IPM/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Amir Akbary DTSTART:20221121T130000Z DTEND:20221121T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/25 DESCRIPTION:Title: Value-distribution of automorphic L-functions\nby Amir Akbary as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nAfter a brief introd uction on the value-distribution of arithmetic functions and L-functions\, we give an overview of our joint work with Alia Hamieh (University of Nor thern British Colombia) on the value-distribution of logarithmic derivativ e of certain automorphic L-functions. Among other things\, we describe an upper bound for the discrepancy of the distribution of the values (at a po int on the edge of the critical strip) of the twists of a fixed automorphi c L-function with quadratic Dirichlet characters. Our result can be consid ered as an automorphic analogue of a result of Lamzouri\, Lester\, and Rad ziwill for the logarithm of the Riemann zeta function. Our estimate is con ditional on certain expected bounds on the local parameters of L-functions which is known to be true for GL(1) and GL(2).\n\nZoom Meeting ID: 856 13 86 0958\nPasscode: 513 992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya DTSTART:20221219T130000Z DTEND:20221219T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/26 DESCRIPTION:Title: Computing Schneider p-adic heights on hyperelliptic Mumford curves\nb y Enis Kaya as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nT here are several definitions of p-adic height pairings on curves in the li terature\, and algorithms for computing them play a crucial role in\, for example\, carrying out the quadratic Chabauty method\, which is a p-adic m ethod that attempts to determine rational points on curves of genus at lea st two.\n\n \n\nThe $p$-adic height pairing constructed by Peter Schneider in $1982$ is particularly important because the corresponding $p$-adic re gulator fits into $p$-adic versions of Birch and Swinnerton-Dyer conjectur e. In this talk\, we present an algorithm to compute the Schneider $p$-adi c height pairing on hyperelliptic Mumford curves. We illustrate this algor ithm with a numerical example computed in the computer algebra system Sage Math.\n\n \n\nThis talk is based on a joint work in progress with Marc Mas deu\, J. Steffen Müller and Marius van der Put.\n\nZoom Meeting ID: 856 1 386 0958\nPasscode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Asgar Jamneshan (Koc University) DTSTART:20221205T130000Z DTEND:20221205T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/27 DESCRIPTION:Title: CANCELLED - On inverse theorems and conjectures in ergodic theory and add itive combinatorics\nby Asgar Jamneshan (Koc University) as part of FG C-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will provide a non-techn ical overview of some interactions between ergodic theory and additive com binatorics. The focus will be on inverse theorems and conjectures for the Gowers uniformity norms for finite abelian groups in additive combinatoric s and their counterparts for the Host-Kra-Gowers uniformity seminorms for abelian measure-preserving systems in ergodic theory.\n\nUnfortunately our speaker cannot make it today due to an emergency. We will reschedule his talk for another time. Sorry for the inconvenience.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Yen-Tsung Chen DTSTART:20230116T130000Z DTEND:20230116T140000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/29 DESCRIPTION:Title: On the partial derivatives of Drinfeld modular forms of arbitrary rank\nby Yen-Tsung Chen as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAb stract\nIn the 1980's\, the study of Drinfeld modular forms for the rank 2 setting was initiated by Goss. Recently\, by the contributions of Basson\ , Breuer\, Häberli\, Gekeler\, Pink et. al.\, the theory of Drinfeld modu lar forms has been successfully generalized to the arbitrary rank setting. In this talk\, we introduce an analogue of the Serre derivation acting on the product of spaces of Drinfeld modular forms of rank r>1\, which also generalizes the differential operator introduced by Gekeler in the rank tw o case. This is joint work with Oğuz Gezmiş.\n\nZoom Meeting ID: 856 138 6 0958\nPasscode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilker Inam DTSTART:20230315T140000Z DTEND:20230315T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/30 DESCRIPTION:Title: Fast Computation of Half-Integral Weight Modular Forms\nby Ilker Inam as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nModular form s continue to attract attention for decades with many different applicatio n areas. To study statistical properties of modular forms\, including for instance Sato-Tate like problems\, it is essential to be able to compute a large number of Fourier coefficients. In this talk\, we will show that th is can be achieved in level 4 for a large range of half-integral weights b y making use of one of three explicit bases\, the elements of which can be calculated via fast power series operations.\nThis is joint work with Gab or Wiese (Luxembourg).\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\ n LOCATION:https://researchseminars.org/talk/FGC-IPM/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Alia Hamieh DTSTART:20230405T140000Z DTEND:20230405T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/32 DESCRIPTION:Title: Moments of $L$-functions and Mean Values of Long Dirichlet Polynomials\nby Alia Hamieh as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr act\nEstablishing asymptotic formulae for moments of $L$-functions is a ce ntral theme in analytic number theory. This topic is related to various no n-vanishing conjectures and the generalized Lindelöf Hypothesis. A major breakthrough in analytic number theory occurred in 1998 when Keating and S naith established a conjectural formula for moments of the Riemann zeta fu nction using ideas from random matrix theory. The methods of Keating and S naith led to similar conjectures for moments of many families of $L$-funct ions. These conjectures have become a driving force in this field which ha s witnessed substantial progress in the last two decades. \nIn this talk\, I will review the history of this subject and survey some recent results. I will also discuss recent joint work with Nathan Ng on the mean values o f long Dirichlet polynomials which could be used to model moments of the z eta function.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Asgar Jamneshan DTSTART:20230419T140000Z DTEND:20230419T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/33 DESCRIPTION:Title: On inverse theorems and conjectures in ergodic theory and additive combin atorics\nby Asgar Jamneshan as part of FGC-HRI-IPM Number Theory Webin ars\n\n\nAbstract\nI will provide a non-technical overview of some interac tions between ergodic theory and additive combinatorics. The focus will be on inverse theorems and conjectures for the Gowers uniformity norms for f inite abelian groups in additive combinatorics and their counterparts for the Host-Kra-Gowers uniformity seminorms for abelian measure-preserving sy stems in ergodic theory.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 51399 2\n LOCATION:https://researchseminars.org/talk/FGC-IPM/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Gupta DTSTART:20230503T140000Z DTEND:20230503T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/34 DESCRIPTION:Title: Tame class field theory\nby Rahul Gupta as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nAs a part of global class field theory\, w e construct a reciprocity map that describes the unramified (resp. tame) étale fundamental group as a pro-completion of a suitable idele class gro up (resp. tame idele class group) for smooth curves over finite fields. Th ese results were extended to higher-dimensional smooth varieties over fini te fields by Kato-Saito (unramified case\, in 1986) and\nSchmidt-Spiess (t ame case\, in 2000). We begin the talk by recalling these results.\n\nThe main focus of the talk is to work with smooth varieties over local fields. The class field theory over local fields is not as nice as that over fini te fields. We discuss results in the unramified class field theory over lo cal fields achieved in the period 1981--2015 by various mathematicians (Bl och\, Saito\, Jennsen\, Forre\, etc.). We then move to the main topic of t he talk which is the tame class field theory over local fields and prove t hat the results in the tame case are similar to that in the case of unrami fied class field theory.\n\nThis talk will be based on a joint work with A . Krishna and J. Rathore.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 5139 92\n LOCATION:https://researchseminars.org/talk/FGC-IPM/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiana Bertolin DTSTART:20230517T140000Z DTEND:20230517T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/35 DESCRIPTION:Title: Periods of 1-motives and their polynomials relations\nby Cristiana Be rtolin as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe in tegration of differential forms furnishes an isomorphism between the De Rh am and the Hodge realizations of a 1-motive M. The coefficients of the mat rix representing this isomorphism are the so-called "periods" of M.\n In t he semi-elliptic case (i.e. the underlying extension of the 1-motive is an extension of an elliptic curve by the multiplicative group)\, we compute explicitly these periods. \n \nIf the 1-motive M is defined over an algebr aically closed field\, Grothendieck's conjecture asserts that the transcen dence degree of the field generated by the periods is equal to the dimensi on of the motivic Galois group of M. If we denote by I the ideal generated by the polynomial relations between the periods\, we have that "the numbe rs of periods of M minus the rank of the ideal I is equal to the dimension of the motivic Galois group of M"\, that is a decrease in the dimension o f the motivic Galois group is equivalent to an increase of the rank of the ideal I. We list the geometrical phenomena which imply the decrease in th e dimension of the motivic Galois group and in each case we compute the po lynomials which generate the corresponding ideal I.\n\nZoom Meeting ID: 85 6 1386 0958 Passcode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlo Pagano DTSTART:20230531T140000Z DTEND:20230531T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/36 DESCRIPTION:Title: Abelian arboreal representations\nby Carlo Pagano as part of FGC-HRI- IPM Number Theory Webinars\n\n\nAbstract\nI will present joint work with A ndrea Ferraguti which makes progress on a Conjecture of Andrews and Petsch e that classifies abelian dynamical Galois groups over number fields\, in the unicritical case. I will explain how to reduce the conjecture to the p ost-critically finite case and the key tools to handle all unicritical PCF with periodic critical orbit over any number field and all PCF over quadr atic number fields. Along the way I will present an earlier rigidity resul t of ours on the maximal closed subgroup of the automorphism group of a bi nary rooted tree\, which offered us with the main input to translate the c ommutativity of the Galois image into diophantine equations. I will also o verview progress on the tightly related problem of lower bounding arboreal degrees.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Olga Lukina (Leiden University) DTSTART:20230614T140000Z DTEND:20230614T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/37 DESCRIPTION:Title: Weyl groups in Cantor dynamics\nby Olga Lukina (Leiden University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nArboreal repres entations of absolute Galois groups of number fields are given by profinit e groups of automorphisms of regular rooted trees\, with the geometry of t he tree determined by a polynomial which defines such a representation. Th us arboreal representations give rise to dynamical systems on a Cantor set \, and allow to apply the methods of topological dynamics to study problem s in number theory. In this talk we consider the conjecture of Boston and Jones\, which states that the images of Frobenius elements under arboreal representations have a certain cycle structure. To study this conjecture\, we borrow from the Lie group theory the concepts of maximal tori and Weyl groups\, and introduce maximal tori and Weyl groups in the profinite sett ing. We then use this new technique to give a partial answer to the conjec ture by Boston and Jones in the case when an arboreal representations is d efined by a post-critically finite quadratic polynomial over a number fiel d. Based on a joint work with Maria Isabel Cortez.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Berkay Kebeci (Koc University) DTSTART:20231025T140000Z DTEND:20231025T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/38 DESCRIPTION:Title: Mixed Tate Motives and Aomoto Polylogarithms\nby Berkay Kebeci (Koc U niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGr othendieck proposed the category of motives as a Tannakian category\, offe ring a universal framework for Weil cohomology theories. In this talk\, we will consider motives in the sense of Nori. One expects the Hopf algebra R of mixed Tate motives to be isomorphic to the bi-algebra A of Aomoto pol ylogarithms. Our aim is to reconstruct A using Nori motives. This allows u s to write a morphism from A to R.\n\nEmail ozlemejderff at gmail.com for the passcode.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertöz (Leiden University) DTSTART:20231206T140000Z DTEND:20231206T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/39 DESCRIPTION:Title: (Cancelled!!!)Computing linear relations between univariate integrals \nby Emre Sertöz (Leiden University) as part of FGC-HRI-IPM Number Theory Webinars\n\nLecture held in https://kocun.zoom.us/j/99715471656.\n\nAbstr act\nThe study of integrals of univariate algebraic functions (1-periods) provided the impetus to develop much of algebraic geometry and transcenden tal number theory. This old saga is now at a point of resolution. In 2022\ , Huber and Wüstholz gave a "qualitative description" of all linear relat ions with algebraic coefficients between 1-periods. New techniques for det ermining symmetries of complex tori allow us to develop algorithms to expl icate these qualitative relations and decide the transcendence of 1-period s. This is a work-in-progress with Joël Ouaknine (MPI SWS) and James Worr ell (Oxford).\n\nThe talk is cancelled.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Koc University) DTSTART:20231011T140000Z DTEND:20231011T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/40 DESCRIPTION:Title: Algebraic Curves from Polygons\nby Türkü Özlüm Çelik (Koc Univer sity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nWe stud y constructing an algebraic curve from a Riemann surface given via a trans lation surface\, which is a collection of finitely many polygons in the pl ane with sides identified by translation. We use the theory of discrete Ri emann surfaces to give an algorithm for approximating the Jacobian variety of a translation surface whose polygon can be decomposed into squares. We first implement the algorithm in the case of L-shaped polygons where the algebraic curve is already known. The algorithm is also implemented in any genus for specific examples of Jenkins-Strebel representatives\, a dense family of translation surfaces that\, until now\, lived on the analytic si de of the transcendental divide between Riemann surfaces and algebraic cur ves. Using Riemann theta functions\, we give numerical experiments and res ulting conjectures up to genus 5.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Soumya Sankar (Utrecht University) DTSTART:20231122T140000Z DTEND:20231122T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/41 DESCRIPTION:Title: Counting points on stacks and elliptic curves with a rational N-isogeny< /a>\nby Soumya Sankar (Utrecht University) as part of FGC-HRI-IPM Number T heory Webinars\n\n\nAbstract\nThe classical problem of counting elliptic c urves with a rational N-isogeny can be phrased in terms of counting ration al points on certain moduli stacks of elliptic curves. Counting points on stacks\, while posing various challenges\, has also opened up several new avenues of exploration in the last few years. In this talk\, I will give a n introduction to modular curves from the stacky perspective\, discuss som e notions of height on them\, and use some of these notions to answer the counting question mentioned above. Time permitting\, I will talk about thi s in the context of the stacky version of the Batyrev-Manin conjecture. Th e talk assumes no prior knowledge of stacks and is based on joint work wit h Brandon Boggess.\n\npassword is eight four eight zero eight four\n LOCATION:https://researchseminars.org/talk/FGC-IPM/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Farzad Aryan DTSTART:20231108T140000Z DTEND:20231108T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/42 DESCRIPTION:Title: Cancellations in Character Sums and the Vinogradov Conjecture\nby Far zad Aryan as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we will explore conjectures related to cancellations in charac ter sums.\nAdditionally\, we will examine the potential impact on the dist ribution of zeros of Dirichlet L-functions if these conjectures prove to b e false.\n\nplease send an email to ozlemejderff at gmail.com for the pass code.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Hamed Mousavi (King's College London) DTSTART:20240306T140000Z DTEND:20240306T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/43 DESCRIPTION:Title: POINTWISE ERGODIC THEOREM ALONG PRIMES\nby Hamed Mousavi (King's Coll ege London) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI n this talk\, we will be exploring the pointwise convergence of ergodic av erages along\nthe primes. Our discussion will begin by explaining the cont ributions of Birkhoff\, as\nwell as the efforts made by Bourgain and Wierd l in this direction\, which was concluded\nby Mirek’s proof of pointwise ergodic convergence for primes. Additionally\, we will be\npresenting som e of our own results on structure theorems in the endpoint case Lplogq\,\n along with a pointwise ergodic theorem in the Gaussian setting. Moving for ward\, we will\nbriefly mention the breakthrough result made by Krause-Mir ek-Tao on bilinear ergodic\naverages. This will be departing point in our current project on the pointwise ergodic\ntheorem for bilinear averages al ong prime numbers. If time allows\, we will provide a toy\nmodel example i n linear theory\, which will demonstrate a typical method used in this\nar ea of study.\n\npassword is 848084.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Myerson (University of Warwick) DTSTART:20240207T140000Z DTEND:20240207T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/44 DESCRIPTION:Title: A two dimensional delta method and applications to quadratic forms\nb y Simon Myerson (University of Warwick) as part of FGC-HRI-IPM Number Theo ry Webinars\n\n\nAbstract\nWe develop a two dimensional version of the del ta symbol method and apply it to establish quantitative Hasse principle fo r a smooth pair of quadrics defined over Q in at least 10 variables. This is a joint work with Pankaj Vishe (Durham) and Junxian Li (Bonn).\n\npassw ord: 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertoz (Leiden University) DTSTART:20240320T140000Z DTEND:20240320T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/45 DESCRIPTION:Title: Computing linear relations between univariate integrals\nby Emre Sert oz (Leiden University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n Abstract\nThe study of integrals of univariate algebraic functions (1-peri ods) provided the impetus to develop much of algebraic geometry and transc endental number theory. This old saga is now at a point of resolution. In 2022\, Huber and Wüstholz gave a "qualitative description" of all linear relations with algebraic coefficients between 1-periods. New techniques fo r determining symmetries of complex tori allow us to develop algorithms to explicate these qualitative relations and decide the transcendence of 1-p eriods. This is a work-in-progress with Joël Ouaknine (MPI SWS) and James Worrell (Oxford).\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Firtina Kucuk (University College\, Dublin) DTSTART:20240403T140000Z DTEND:20240403T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/46 DESCRIPTION:Title: Factorization of algebraic p-adic Rankin-Selberg L-functions\nby Firt ina Kucuk (University College\, Dublin) as part of FGC-HRI-IPM Number Theo ry Webinars\n\n\nAbstract\nI will give a brief review of Artin formalism a nd its p-adic variant. Artin formalism gives a factorization of L-function s whenever the associated Galois representation decomposes. I will explain why establishing the p-adic Artin formalism (or its algebraic counterpart via the Iwasawa Main Conjectures) is a non-trivial problem when there are no critical L-values. In particular\, I will focus on the case where the Galois representation arises from a self-Rankin-Selberg product of a newfo rm\, and present the results in this direction including the one I obtaine d in my PhD thesis.\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Haydar Goral (Izmir Institute of Technology) DTSTART:20240221T140000Z DTEND:20240221T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/47 DESCRIPTION:Title: Counting arithmetic progressions modulo p\nby Haydar Goral (Izmir Ins titute of Technology) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nA bstract\nIn 1975\, Szemeredi gave an affirmative answer to Erdös and Tura n's conjecture which states that any subset of positive integers with a po sitive upper density contains arbitrarily long arithmetic progressions. Sz emeredi-type problems have also been extensively studied in subsets of fin ite fields. While much work has been done on the problem of whether subset s of finite fields contain arithmetic progressions\, in this talk we conce ntrate on how many arithmetic progressions we have in certain subsets of f inite fields. The technique is based on certain types of Weil estimates. W e obtain an asymptotic for the number of k-term arithmetic progressions in squares with a better error term. Moreover our error term is sharp and be st possible when k is small\, owing to the Sato-Tate conjecture. This work is supported by the Scientific and Technological Research Council of Turk ey with the project number 122F027.\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmed El-Guindy (Cairo University) DTSTART:20241024T133000Z DTEND:20241024T143000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/48 DESCRIPTION:Title: Some l-adic properties of modular forms with quadratic nebentypus and l-r egular partition congruences\nby Ahmed El-Guindy (Cairo University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we discuss a framework for studying l-regular partitions by defining a seq uence of\nmodular forms of level l and quadratic character which encode th e l-adic behavior of the so-called l-regular\npartitions. We show that thi s sequence is congruent modulo increasing powers of l to level 1 modular f orms of\nincreasing weights. We then prove that certain modules generated by our sequence are isomorphic to certain\nsubspaces of level 1 cusp forms of weight independent of the power of l\, leading to a uniform bound on t he\nranks of those modules and consequently to l-adic relations between l- regular partition values. This\ngeneralizes earlier work of Folsom\, Kent and Ono on the partition function\, where the relevant forms had no\nneben typus\, and is joint work with Mostafa Ghazy.\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Erman Isik (The Univ. of Ottowa) DTSTART:20241106T133000Z DTEND:20241106T143000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/49 DESCRIPTION:Title: The growth of Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic Zp- extensions at inert primes\nby Erman Isik (The Univ. of Ottowa) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr act\nIn this talk\, we will discuss the asymptotic growth of both the Mord ell-Weil ranks and the Tate–Shafarevich groups for an elliptic curve E d efined over the rational numbers\, focusing on its behaviour along the ant icyclotomic Zp-extension of an imaginary quadratic K. Here\, p is a prime at which E has good supersingular reduction and is inert in K. We will rev iew the definitions and properties of the plus and minus Selmer groups fro m Iwasawa theory and discuss how these groups can be used to derive arithm etic information about the elliptic curve.\n\nhttps://kocun.zoom.us/j/9971 5471656\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Amina Abdurrahman (IHES) DTSTART:20241120T133000Z DTEND:20241120T143000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/50 DESCRIPTION:Title: A formula for symplectic L-functions and Reidemeister torsion\nby Ami na Abdurrahman (IHES) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nA bstract\nWe give a global cohomological formula for the central value of t he L-function of a symplectic representation on a curve up to squares. The proof relies crucially on a similar formula for the Reidemeister torsion of 3-manifolds together with a symplectic local system. We sketch both ana logous arithmetic and topological pictures. This is based on joint work wi th A. Venkatesh.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Ferraguti (Università di Torino) DTSTART:20241204T140000Z DTEND:20241204T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/51 DESCRIPTION:Title: Frobenius and settled elements in iterated Galois extensions\nby Andr ea Ferraguti (Università di Torino) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nUnderstanding Frobenius elements in iterated Galoi s extensions is a major goal in arithmetic dynamics. In 2012 Boston and Jo nes conjectured that any quadratic polynomial f over a finite field that i s different from x^2 is settled\, namely the weighted proportion of f-stab le factors in the factorization of the n-th iterate of f tends to 1 as n t ends to infinity. This can be rephrased in terms of Frobenius elements: gi ven a quadratic polynomial f over a number field K\, an element \\alpha in K and the extension K_\\infty generated by all the f^n-preimages of \\alp ha\, the Frobenius elements of unramified primes in K_\\infty are settled. In this talk\, we will explain how to construct uncountably many non-conj ugate settled elements that cannot be the Frobenius of any ramified or unr amified prime\, for any quadratic polynomial. The key result is a descript ion of the critical orbit modulo squares for quadratic polynomials over lo cal fields. This is joint work with Carlo Pagano.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomos Parry (Bilkent University) DTSTART:20241218T140000Z DTEND:20241218T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/52 DESCRIPTION:Title: Primes in arithmetic progressions on average\nby Tomos Parry (Bilkent University) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TB A\n LOCATION:https://researchseminars.org/talk/FGC-IPM/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmet Guloglu (Bilkent University) DTSTART:20250129T140000Z DTEND:20250129T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/53 DESCRIPTION:Title: Non-vanishing of L-functions at the central point.\nby Ahmet Guloglu (Bilkent University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAb stract\nI will talk about two methods used to derive non-vanishing results for a family of L-functions\; the one-level density and the moments of L- functions. I will mention what these methods are and how they are used to get non-vanishing.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Ratko Darda (Sabanci University) DTSTART:20250212T140000Z DTEND:20250212T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/54 DESCRIPTION:Title: Malle conjecture for finite group schemes\nby Ratko Darda (Sabanci Un iversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe Inverse Galois Problem asks whether every finite group G is the Galois gr oup of a Galois extension of the field of rational numbers Q. The Malle co njecture offers a quantitative perspective: it predicts the number of Galo is extensions of Q (or any other number field)\, with G as the Galois grou p\, of bounded "size" (such as the discriminant). In this talk\, we explo re a generalization of the conjecture to finite étale group schemes. We s how how the generalization helps explain inconsistencies of the Malle conj ecture found by Klüners. Additionally\, we discuss the case of the conjec ture when G is a commutative finite étale group scheme\, which generalize s the classical work of Wright on the number of abelian extensions of boun ded discriminant. The talk is based on a joint work with Takehiko Yasuda.\ n LOCATION:https://researchseminars.org/talk/FGC-IPM/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Keerthi Madapusi (Boston College) DTSTART:20250226T140000Z DTEND:20250226T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/55 DESCRIPTION:Title: A new approach to p-Hecke correspondences and Rapoport-Zink spaces\nb y Keerthi Madapusi (Boston College) as part of FGC-HRI-IPM Number Theory W ebinars\n\n\nAbstract\nWe will present a new notion of isogeny between ‘ p-divisible groups with additional structure’ that employs the cohomolog ical stacks of Drinfeld and Bhatt-Lurie—-in particular the theory of ape rtures developed in prior work with Gardner—-and combines it with some i nvariant theoretic tools familiar to the geometric Langlands and represent ation theory community\, namely the Vinberg monoid and the wonderful compa ctification. This gives a uniform construction of p-Hecke correspondeces a nd Rapoport-Zink spaces associated with unramified local Shimura data. In particular\, we give the first general construction of RZ spaces associate d with exceptional groups. This work is joint with Si Ying Lee.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Bartling DTSTART:20250507T140000Z DTEND:20250507T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/56 DESCRIPTION:Title: Rapoport-Zink spaces and close p-adic fields.\nby Sebastian Bartling as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nRapoport-Zink spaces are moduli spaces of p-divisible groups\n(with extra structure). T hese are p-adic analogues of integral models of\nShimura varieties. Their function field versions were introduced by\nHartl-Viehmann. I want to expl ain a construction approximating\nHartl-Viehmann spaces via Rapoport-Zink spaces using the philosophy of\nclose p-adic fields. If time permits I wan t to sketch how one may use\nthis construction to deduce the Arithmetic Fu ndamental Lemma in the\nfunction field case. This is joint work\, partly i n progress\, with\nAndreas Mihatsch.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirti Joshi (University of Arizona) DTSTART:20251009T160000Z DTEND:20251009T170000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/57 DESCRIPTION:Title: Deformations of arithmetic of number fields and the abc-conjecture\nb y Kirti Joshi (University of Arizona) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this lecture I will provide an accessible over view of my\nrecent work on deformation of arithmetic of number fields (as\ nsuggested by Shinichi Mochizuki) and its relationship to the\nabc-conject ure following Mochizuki's strategy for its proof.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Ferruh Özbudak (Sabanci University) DTSTART:20251022T140000Z DTEND:20251022T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/58 DESCRIPTION:Title: Some Results on Covering Radius of Codes\nby Ferruh Özbudak (Sabanci University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\n The covering radius is an important parameter in coding theory. In this ta lk\,\nwe present several results concerning the covering radius of various classes of codes\,\nobtained using techniques involving algebraic curves over finite fields. Connections to algebra\, number theory\,\nand geometry will also be discussed.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Anette Huber-Klawitter (University of Freiburg) DTSTART:20251105T140000Z DTEND:20251105T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/59 DESCRIPTION:Title: Motives and transcendence\nby Anette Huber-Klawitter (University of F reiburg) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nPeri ods are complex numbers defined by integrating algebraic differential form s over paths (on algebraic varieties) with algebraic end points. The set c ontains many interesting numbers like \nlog(2) or π that have been studie d intensely in transcendence theorem. By the linear version of the Period Conjecture (a theorem of Wüstholz and myself in this case)\, all relation s between them are described in terms of 1-motives. In this expository tal k\, we will explain this result and give a couple of examples.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Ertan Elma (Mathematics Research Center-Azerbaijan State Oil and I ndustry University) DTSTART:20251119T150000Z DTEND:20251119T160000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/60 DESCRIPTION:Title: Number of prime factors with a given multiplicity\nby Ertan Elma (Mat hematics Research Center-Azerbaijan State Oil and Industry University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nFor natural numb ers $k\, n \\ge 1$\, let $\\omega_k(n)$ be the number of prime factors of $n$ with multiplicity $k$. The functions $\\omega_k(n)$ with $k \\ge 1$ ar e refined versions of the well-known function $\\omega(n)$ counting the nu mber of distinct prime factors of $n$ without any conditions on the multip licities. In this talk\, we will cover several elementary\, analytic and p robabilistic results about the functions $\\omega_k(n)$ with $k \\ge 1$ an d their function field analogues in polynomial rings with coefficients fro m a finite field. In particular\, we will see that the function $\\omega_1 (n)$ and its function field analogue satisfy the Erd\\H{o}s--Kac Theorem. The results we will see in this talk are based on joint works with Yu-Ru L iu\, with Sourabhashis Das\, Wentang Kuo and Yu-Ru Liu\, and with Greg Mar tin.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/60/ END:VEVENT BEGIN:VEVENT SUMMARY:James Borger DTSTART:20251203T090000Z DTEND:20251203T095000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/61 DESCRIPTION:Title: Scheme Theory over Semirings\nby James Borger as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nUsual scheme theory can be viewed as the syntactic theory of\npolynomial equations with coefficients in a ring \, most importantly the\nring of integers. But none of its most fundamenta l ingredients\, such\nas\nfaithfully flat descent\, require subtraction. S o we can set up a\nscheme theory over semirings (``rings but possibly with out additive\ninverses’’\, such as the non-negative integers or reals) \, thus\nbringing positivity in to the foundations of scheme theory. It is then\nreasonable to view non-negativity as integrality at the infinite\np lace\, the Boolean semiring as the residue field there\, and the non-negat ive\nreals as the completion.\n\n In this talk\, I'll discuss some recent developments in module theory\n over semirings. While the classical defini tions of ``vector bundle''\n are\nnot all equivalent over semirings\, the classical definitions of ``line\nbundle'' are all equivalent\, which allow s us to define Picard groups\nand\nPicard stacks. The narrow class group o f a number field can be\nrecovered\nas the reflexive class group of the se miring of its totally\n nonnegative\nintegers\, i.e. the arithmetic compac tification of the spectrum of the\nring of integers. This gives a scheme-t heoretic definition of the\nnarrow\nclass group\, as was done for the ordi nary class group a long time ago.\n\nThis is based mostly on arXiv:2405.18 645\, which is joint work with\n Jaiung Jun\, and also on forthcoming pape r with Johan de Jong and Ivan\nZelich.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Lejla Smajlovic DTSTART:20251217T140000Z DTEND:20251217T150000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/62 DESCRIPTION:Title: On some nonholomorphic automorphic forms\, their inner products and gener ating functions\nby Lejla Smajlovic as part of FGC-HRI-IPM Number Theo ry Webinars\n\n\nAbstract\nIn this talk we focus on the following three au tomorphic forms on a Fuchsian group of the first kind with at least one cu sp: the Eisenstein series and the Niebur-Poincaré series associated to th e cusp at infinity\, and the resolvent kernel/Green's function. We discuss how those functions can be viewed as building blocks for describing log-n orms of some meromorphic functions in terms of their divisors and derive a generalization of the Rorlich-Jensen type formula\, which is based on an evaluation of the Petersson inner product of the Niebur-Poincaré series w ith the suitably regularized Green's function. Then\, we turn our attentio n to the generating functions of the Niebur-Poincaré series and its deriv ative at s=1. Both functions depend upon two variables in the upper half-p lane. We prove that\, for any Fuchsian group of the first kind\, the gener ating function of the Niebur-Poincaré series in each variable is a polar harmonic Maass form of a certain weight\, describe its polar part and disc uss how it can be viewed as a building block for describing weight two mer omorphic modular forms in terms of their divisors. Moreover\, we prove tha t the generating function of the derivative of the Niebur-Poincaré series at s=1 can be expressed\, up to a certain function appearing in the Krone cker limit formula\, as a derivative of an automorphic kernel associated t o a new point-pair invariant expressed in terms of the Rogers dilogarithm. \n\nThe talk is based on the joint work with Kathrin Bringmann\, James Cog dell and Jay Jorgenson.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Kübra Benli (Bogazici University) DTSTART:20260114T160000Z DTEND:20260114T170000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/63 DESCRIPTION:Title: Sums of proper divisors with missing digits\nby Kübra Benli (Bogazic i University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\ nLet $s(n)$ denote the sum of proper divisors of a positive integer $n$. I n 1992\, Erd\\H{o}s\, Granville\, Pomerance\, and Spiro conjectured that i f $\\mathcal{A}$ is a set of integers with asymptotic density zero then th e preimage set $s^{-1}(\\mathcal{A})$ also has asymptotic density zero. In this talk\, we will discuss the verification of this conjecture when $\\m athcal{A}$ is the set of integers with missing digits (also known as elli psephic integers) by giving a quantitative estimate on the size of the set $s^{-1}(\\mathcal{A})$. This talk is based on the joint work with Giulia Cesana\, C\\'{e}cile Dartyge\, Charlotte Dombrowsky\, Paul Pollack and Lol a Thompson.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Lochak DTSTART:20260128T160000Z DTEND:20260128T170000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/64 DESCRIPTION:Title: A historical introduction to Grothendieck-Teichmüller theory\nby Pie rre Lochak as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nSt arting with the statement of Belyi's theorem\, I will explain\nhow Grothen dieck-Teichmüller theory was born\, then move\nto a (necessarily incomple te) exposition of its main tenets\,\nthe already existing results and the main conjectures.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg German DTSTART:20260211T190000Z DTEND:20260211T195000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/65 DESCRIPTION:Title: On the transference principle in Diophantine approximation\nby Oleg G erman as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn 1842 \, Dirichlet published his famous theorem which became\nthe foundation of Diophantine approximation. The phenomenon he found\ninspired Liouville to study how well algebraic numbers can be\napproximated by rationals\, and t hus\, to come up with a method of\nconstructing transcendental numbers exp licitly. The development of these\nideas led to the concepts of irrational ity measure and transcendence\nmeasure. Thanks to Minkowski\, it became cl ear that many problems arising\nin the theory of Diophantine approximation could be addressed quite\neffectively using the tools of geometry of numb ers. In particular\, the\ngeometric approach naturally offers a wide varie ty of multidimensional\nanalogues of the concept of irrationality measure — so called\nDiophantine exponents. In the talk\, we will discuss variou s Diophantine\nexponents and the geometry that arises when studying them. We will pay\nspecial attention to the phenomenon discovered by Khintchine\ , which he\ncalled the transference principle.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Özge Ülkem (Academia Sinica\, Taipei) DTSTART:20260225T100000Z DTEND:20260225T110000Z DTSTAMP:20260314T090017Z UID:FGC-IPM/66 DESCRIPTION:Title: Drinfeld's Elliptic Sheaves and Generalizations\nby Özge Ülkem (Aca demia Sinica\, Taipei) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n Abstract\nIn this talk\, we will explore the area of function field\narith metic\, with a focus on Drinfeld's elliptic sheaves and their\ngeneralizat ions\, as well as analogies to the number field setting.\nDrinfeld modules \, introduced in 1974 as analogues of elliptic curves in\nthe function fie ld setting\, play a central role in this context. To\nestablish a Langland s correspondence\, Drinfeld studied moduli spaces of\nelliptic sheaves\, o r equivalently\, shtukas. After a brief introduction\nto the function fiel d framework\, we will examine some well-known\ngeneralizations of elliptic sheaves\, concentrating on generalized\nD-elliptic sheaves and presenting results on their moduli spaces. In the\nfinal part of the talk\, we will explore the connections between\n(generalized) shtukas and (generalized) e lliptic sheaves.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/66/ END:VEVENT END:VCALENDAR