Link to 1st FGC-IPM Joint Number Theory Meeting website at FGC
Link to 2nd FGC-IPM Joint Mini Workshop “Arithmetic of Local and Global Fields”
Link to IPM School of Mathematics
Link to IPM
IPM Number Theory website
Link to HRI
 

Starting on 31.01.2021, Harish-Chandra Research Institute (HRI) has joined in the FGC-IPM number theory network. From now on the number theory seminars being conducted will be named FGC-HRI-IPM Number theory seminars.
FGC and IPM jointly organized a Number Theory Meeting on March 15 - 17, 2021. There is a link above to this event which formed the genesis of biweekly FGC-IPM number theory seminars.
Number Theory meetings will reconvene for Fall 2021 semester starting on September 28 2021.

FGC-IPM Joint Number Theory Webinars for 2023 

Speaker: Yen-Tsung Chen
Title: On the Partial Derivatives of Drinfeld Modular Forms of arbitrary rank
Time: 16 January

Speaker: Ilker Inam
Title: Fast Computation of Half Integral Weight Modular Forms
Time: 15 March

Speaker: Alia Hamieh
Title: Moments of L-functions and Mean Values of Long Drichlet Polynomials
Time: 5 April

Speaker: Asgar Jamneshan
Title: On Inverse Theorems and Conjectures in Ergodic Theory
Time: 19 April

Speaker: Rahul Gapta
Title: Tame Class Field Theory
Time: 3 May

Speaker: Cristiana Bertolin
Title: Periods of 1-motives and their polynomial relations
Time: 17 May

Speaker: Carlo Pagano
Title: Abelian Arboreal Representations
Time: 31 May

Speaker: Olga Lukina
Title: Weyl Groups in Cantor Dynamics
Time: 14 June

Speaker: Turku Ozlum Celik
Title: Algebraic Curves From Polygons
Time: 11 October

Speaker: Berkay Kebeci
Title: Mixed Tate Motives and Aomoto Polylogarithms
Time: 25 October

Speaker: Farzad Aryan
Title: Cancellations in Character Sums and the Vinogradov Conjecture
Time: 8 November

Speaker: Soumya Sankar
Title: Counting Points on Stacks and Elliptic Curves with a rational N-isogeny
Time: 22 November

Speaker: Emre Sertoz
Title: Computing Linear Relations between Univariate integrals
Time: 6 December

FGC-IPM Joint Number Theory Webinars for Winter-Spring 2022 Semester

Speaker: Somnath Jha (IIT Kanpur, India)
Title: Fine Selmer group of elliptic curves over global fields
Time:Tuesday May 31, 2022, 15:00 Istanbul | 16:30 Tehran | 17:30 Allahabad.
Zoom link
Passcode: 362880


Speaker: Hamza Yesilyurt (Bilkent University, Ankara, Turkey)
Title: A Modular Equation of Degree 61
Time: Tuesday May17, 2022, 15:00 Istanbul | 16:30 Tehran | 17:30 Allahabad.
Video link


Speaker: Chirantan Chowdhury (University of Duisburg-Essen)
Title: Motivic Homotopy Theory of Algebraic Stacks
Time: Tuesday April 19, 2022, 15:00 Istanbul; 16:30 Tehran; 17:30 Allahabad.
Video link


Speaker: Farzad Aryan (Göttingen University)
Title: On the Riemann Zeta Function
Time: Tuesday April 5, 2022, 15:00 İstanbul time 16:30 Tehran time 17:30 Allahabad time.
Video link


Speaker: Semih Özlem (Yeditepe University)
Title: On the motivic Galois group of a number field
Time: Tuesday March 15, 2022, 16:00 İstanbul time 16:30 Tehran time 18:30 Allahabad time.
Video link
Seminar Notes

Speaker: Gonzalez-Aviles (Universidad de La Serena, Chile)
Title: Totally singular algebraic groups
Time: Tuesday February 1, 2022, 16:30 Tehran time; 16:00 Istanbul time.
Slides
Video link
 

FGC-IPM Joint Number Theory Webinars for Fall 2021 Semester

First Meeting of Fall 2021 semester
Speaker: Professor Ramin Takloo-Bighash (University of Illinois at Chicago)
Title: TBA
Time: Sep 28, 2021 07:30 PM Tehran
Video link

Second Meeting of Fall 2021 semester
Speaker: Professor Mark Kisin (Harvard University)
Title: Essential dimension via prismatic cohomology
Time: Tuesday October 12, 2021, 17:30 Tehran time (17:00 Istanbul-10:00 AM Boston)
Video link

Third Meeting of Fall 2021 semester
Speaker: Reza Taleb (Shahid Beheshti University)
Title: The Coates-Sinnott Conjecture
Time: Tuesday, October 26, 2021 17:30 Tehran time (17:00 Istanbul)
Slides
Video link

Speaker: Shabnam Akhatri (University of Oregon)
Title: TBA
Time: Tuesday, November 9, 2021 17:30 Tehran time (17:00 Istanbul)
Slides
Video link

Speaker: Ali Mohammadi (IPM)
Title: Bounds on point-conic incidences over finite fields and applications
Time: Tuesday, November 23, 2021 15:00 Tehran time (14:30 Istanbul)
Slides
Video link

Speaker: Andrzej Dabrowski (University of Szczecin)
Title: On a class of generalized Fermat equations of signature (2,2n,3)
Time: Tuesday, December 7, 2021 15:00 Tehran time (14:30 Istanbul)
Video link
Seminar Notes 1
Seminar Notes 2

Speaker: Amir Ghadermarzi (University of Tehran)
Title: TBA
Time: Tuesday, December 21, 2021 17:30 Tehran time (17:00 Istanbul)
https://us06web.zoom.us/j/9086116889?pwd=WGRFOGZWZ1FOMXJrcWpJMWFqUFIvQT09
Meeting ID: 908 611 6889
Passcode: 362880

Speaker: Fatma Cicek (IIT Gandhinagar)
Title: Selberg’s Central Limit Theorem
Time: Tuesday, January 4, 2022 17:30 Tehran time (17:00 Istanbul)
Slides

Information about previous meetings, Spring 2021

These seminars will take place on every other Tuesday starting on Tuesday April 27, 2021 at 16:00 Istanbul local time and 17:30 Tehran local time over zoom, allowing for exceptions in scheduling. See the table below for details.
Below is the needed information to participate in these seminars:
Zoom Meeting Link:
https://zoom.us/j/9299700405?pwd=QXZJYTVkeHpJWDE4SGVTbkVzZmJxQT09
Meeting ID: 929 970 0405
Passcode: 210609
Next meeting: June 29, 2021 16:00 Istanbul local time, 17:30 Tehran local time
Speaker: Emre Alkan, Koç Üniversitesi
Title: A history of Asymptotic Formulas in Prime Number Theory
The seminar lasts about an hour, (maximum two hours).
The client for zoom meetings can be downloaded at https://zoom.us/download
If you have any questions, suggestions, feedback regarding the seminars please email the organizers at
fgc.ipm.math at gmail.com
Titles and abstracts of the first seven talks are at the bottom of the page.
Talk 1 | Talk 2 | Talk 3 | Talk 4 | Talk 5 | Talk 6 | Talk 7
Slides and videos of the seminars are below:
Talk 1: Polya and Pre-Polya Groups in Dihedral Number Fields, Abbas Maarefparvar.
Slides | Video
Talk 2: Shimura varieties modulo p with many compact factors, Oliver Bueltel.
Slides | Video
Talk 3: SOLVING FERMAT TYPE EQUATIONS VIA MODULAR APPROACH, Yasemin Kara.
Slides
Talk 4: Étale construction of critical p-adic L-functions and heights on thick Selmer groups, Kazım Büyükboduk.
Slides | Video
Talk 5: Effective height bounds for odd-degree totally real points on some curves, Levent Alpöge, Columbia University.
Slides | Video | Video link at IPM
Talk 6: A history of Asymptotic Formulas in Prime Number Theory, Emre Alkan, Koç Üniversitesi.
Slides | Video
Talk 7: On Drinfeld modular forms of higher rank and quasi-periodic functions, Oğuz Gezmiş, National Tsing Hua University.
Slides | Video

List of Seminars

FGC-IPM Number Theory Seminars 2021

Titles and Abstracts of the first seven talks

Talk 1

Speaker: Abbas Maarefparvar, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran.
Email address: a.marefparvar@ipm.ir
Seminar Date: April 27, 2021
Title: PÓLYA AND PRE-PÓLYA GROUPS IN DIHEDRAL NUMBER FIELDS
Abstract: For a number field K with the ideal class group Cl(K), Pólya group of K is the subgroup Po(K) of Cl(K) generated by the classes of Ostrowski ideals Π _q(K) , where q ≥ 1 is a prime power integer and Π _q(K) denotes the product of all maximal ideals of K with norm q. K is called a Pólya field, Whenever Po(K) is trivial. Pólya fields are a generalization of PID (class number one) number fields, and classically they are defined in terms of regular bases for rings of integer valued polynomials due to George Pólya. For Galois number fields K, investigating on Pólya-ness can be expressable in terms of the action of the Galois group on the ideal class group: Po(K) and the subgroup of Cl(K) generated by the strongly ambiguous ideal classes coincide. In particular, Zantema (whose paper is a great contribution in this subject) showed that in the Galois case, Pólya groups are controllable part of ideal class groups throughout Galois cohomology and ramification. Beside, investigating on Pólya groups in the non-Galois number fields (the more difficult situation), Chabert introduced the notion of pre-Pólya group Po(-) _nr , which is a generalization of the pre-Pólya condition, duo to Zantema. The first part of my talk would be about some results of a joint work with Ali Rajaei, where using Zantema’s result and the arithmetic in ramification theory, we found some results on Pólya groups of dihedral extensions of ℚ of order 2l, for l an odd prime. In the second part, I’ll talk about my recently results on the pre-Pólya group of a D_n-field K, for n ≥ 4 an even integer, where D_n denotes the dihedral group of order 2n.

Talk 2

Speaker: Oliver Bueltel, Universität Duisburg-Essen
Seminar Date: May 11, 2021
Title: Shimura varieties modulo p with many compact factors
Abstract: We give several new moduli interpretations of the special fibres of several Shimura varieties over certain prime numbers. As a corollary we obtain, that for every prescribed odd characteristic p every bounded symmetric domain possesses quotients by arithmetic subgroups, whose models have good reduction at a prime divisor of p.

Talk 3

Speaker: Yasemin Kara, Boğaziçi Üniversitesi (Bosphorus University)
Seminar Date: May 25, 2021
Title: SOLVING FERMAT TYPE EQUATIONS VIA MODULAR APPROACH
Abstract: Recent work of Freitas and Siksek showed that an asymptotic version of Fermat’s Last Theorem (FLT) holds for many totally real fields. This result was extended by Deconinck to the generalized Fermat equation of the form Ax^p + By^p + Cz^p = 0, where A, B, C are odd integers belonging to a totally real field. Later Sengun and Siksek showed that the asymptotic FLT holds over number fields assuming standard modularity conjectures. Combining their techniques we* show that the generalized Fermat’s Last Theorem (GFLT) holds over number fields asymptotically assuming the standard conjectures. We also give three results which show the existence of families of number fields on which asymptotic versions of FLT or GFLT hold. In particular, we prove that the asymptotic GFLT holds for a set of imaginary quadratic number fields of density 5/6. In a different work, we** show that for a totally real number field K with narrow class number one, the Fermat type equation x^p + y^p = z² does not have certain type of solutions in the ring of integers of K for any prime exponent p > B_K where B_K is a constant depending only on K. *joint work with E. Özman ** joint work with E.Isik, E. Özman

Talk 4

Speaker: Kazım Büyükboduk, University College Dublin
Seminar Date: June 8, 2021
Title: Étale construction of critical p-adic L-functions and heights on thick Selmer groups
Abstract: In joint work with Denis Benois, we give an étale construction of Bellaïche's p-adic L-functions about θ-critical points on the Coleman–Mazur eigencurve. I will discuss applications of this construction towards p-adic Gross–Zagier formulae in terms of p-adic heights on what we call the thick Selmer groups, which come attached to the infinitesimal deformation at the said θ-critical point along the eigencurve. Besides our interpolation of the Beilinson–Kato elements about this point (which rests upon the overconvergent étale cohomology of Andreatta–Iovita–Stevens), the key input to prove the interpolative properties of our p-adic L-function is a new p-adic Hodge-theoretic "eigenspace-transition via differentiation" principle. Other notes: For the interested: parts of this work have been announced as arXiv:2008.12536.

Talk 5

Speaker: Levent Alpöge, Columbia University
Seminar Date: June 22, 2021
Title: Effective height bounds for odd-degree totally real points on some curves.
Abstract: We use potential modularity theorems to prove, for a class of smooth projective hyperbolic curves, effective height bounds for all rational points on such curves which are defined over an odd-degree totally real field. (Over such fields and for such curves this amounts to an unconditional effectivization of Faltings’ theorem.) We do this by proving effective height bounds for S-integral K-points on Hilbert modular varieties when K is totally real of odd degree (a familiar hypothesis from the theory of Hilbert modular forms), and then deducing a height bound for rational points on complete curves inside such varieties. The curves C _t : x⁶ + 4y³ = t² (with t a nonzero totally real algebraic number of odd degree, e.g. t = 1) are examples of curves to which this method applies.

Talk 6

Speaker: Emre Alkan, Koç Üniversitesi
Seminar Date: June 29, 2021
Title: A history of Asymptotic Formulas in Prime Number Theory
Abstract: We will present a survey of asymptotic formulas for prime counting functions. Time permitting, we discuss some recent results on this topic from a function theoretic point of view together with historical remarks.

Talk 7

Speaker: Oğuz Gezmiş, National Tsing Hua University
Seminar Date:July 6, 2021
Title: On Drinfeld modular forms of higher rank and quasi-periodic functions
Abstract: In 1980s, David Goss introduced Drinfeld modular forms in the rank two case and revealed several similarities between them and the classical modular forms as well as giving a recipe for how to construct them for the higher rank setting. Later on their higher rank generalization was studied extensively by Basson, Breuer, Gekeler and Pink. In this talk, we introduce a special function on the Drinfeld period domain in the higher rank setting which also generalizes the false Eisenstein series of Gekeler. We also introduce its functional equation, its relation with quasi-periodic functions of a Drinfeld module and the transcendence of its values at CM points. This is a joint work with Yen-Tsung Chen.