The Ohio State University Number Theory Seminar 10/26/2021 10:15am-11:15am (*note unusual day and time*) - Jack Thorne (University of Cambridge) - Symmetric power functoriality for holomorphic modular forms (abstract) Mondays 4:15pm MW 154 (building photo)

 Availability Change months Key Available Booked No Seminar Weekend/Holiday Availability Calendar Organizers Jim Cogdell Ghaith Hiary Roman Holowinsky Wenzhi Luo Jennifer Park Stefan Patrikis Warren Sinnott
 Scheduled Talks Seminars will be held online via Zoom unless otherwise indicated on the schedule. For the link, please email patrikis.1 at osu.edu. 10/26/2021, 10:15am-11:15am (note unusual day and time) - Jack Thorne (University of Cambridge) - Symmetric power functoriality for holomorphic modular forms (abstract) Symmetric power functoriality is the first interesting case of Langlands’s functoriality conjectures and is closely connected to other problems in number theory, such as the Ramanujan conjecture and the Sato—Tate conjecture for elliptic curves. I will discuss the historical motivation for the problem and joint work with James Newton that solves the problem for holomorphic elliptic modular forms. 11/1/2021 - Félix Baril Boudreau (Western University) - Computing an L-function modulo a prime (abstract) 11/8/2021 - No seminar: Danny Krashen (University of Pennsylvania) will speak in the Algebra Seminar. 11/15/2021 - Jacob Tsimerman (University of Toronto) - TBD (abstract) 11/22/2021 - Sarah Arpin (University of Colorado, Boulder) - TBD (abstract) 11/29/2021 - Levent Alpöge (Harvard University) - TBD (abstract) 12/6/2021 - Lue Pan (University of Chicago) - TBD (abstract) 12/13/2021 - Eun Hye Lee (Stony Brook University) - TBD (abstract) 1/24/2022 - Yunqing Tang (Princeton University) - TBD (abstract) 2021-2022 10/18/2021 *in-person: MW154*- Pan Yan (OSU) - $L$-function for $\text{Sp}(4)\times \text{GL}(2)$ via a non-unique model (abstract) 10/11/2021 - Debanjana Kundu (University of British Columbia) - Arithmetic Statistics of Iwasawa Invariants (abstract) 10/4/2021 - Ariel Weiss (Hebrew University of Jerusalem) - Prime torsion in the Tate-Shafarevich groups of abelian varieties over $\mathbb{Q}$ (abstract) 9/20/2021 - Jacob Mayle (University of Illinois at Chicago) - On the effective open image theorem (abstract) 9/13/2021 - Chi-Yun Hsu (UCLA) - Partial classicality of Hilbert modular forms (abstract) 2020-2021 4/19/2021 - Sug Woo Shin (UC Berkeley) - On GSpin(2n)-valued automorphic Galois representations (abstract) 4/5/2021 - Jiuya Wang (Duke University) - Pointwise Bound for $\ell$-torsion of Class Groups (abstract) 3/22/2021 - Hyuk Jun Kweon (MIT) - Bounds on the Torsion Subgroups of Néron-Severi Group Schemes (abstract) 3/1/2021 - Lynnelle Ye (Stanford University) - Properness of Hilbert modular eigenvarieties (abstract) 2/22/2021 - Soumya Sankar (OSU) - Counting elliptic curves with a rational N-isogeny (abstract) 2/15/2021 - Manami Roy (Fordham University) - Counting cuspidal automorphic representation of GSp(4) and its application. (abstract) 2/1/2021 - Eric Stubley (University of Chicago) - Locally Split Galois Representations and Hilbert Modular Forms of Partial Weight One (abstract) 1/25/2021 - Patrick Allen (McGill University) - Modularity of some PGL(2,5) representations (abstract) 11/23/2020 - Caleb Springer (Penn State University) - Abelian varieties and their endomorphism rings (abstract) 11/9/2020 - Guillermo Mantilla-Soler (Aalto University) - A complete invariant for real S_n number fields (abstract) 11/2/2020 - Matilde Lalín (Université de Montréal) - Nonvanishing for cubic L-functions over function fields. (abstract) 10/26/2020 - Naser Talebizadeh Sardari (MPIM) - Vanishing Fourier Coefficients of Hecke Eigenforms (abstract) 10/19/2020 - Efthymios Sofos (University of Glasgow) - Schinzel Hypothesis with probability 1 and rational points (abstract) 10/12/2020 - Shiva Chidambaram (University of Chicago) - Abelian surfaces with fixed 3-torsion (abstract) 10/5/2020 - Koji Shimizu (UC Berkeley) - A p-adic monodromy theorem for de Rham local systems (abstract) 9/28/2020 - Rachel Newton (University of Reading) - Evaluating the wild Brauer group (abstract) 09/21/2020 - Simon Marshall (University of Wisconsin) - Counting cohomological cusp forms on GL_3 (abstract) 09/14/2020 - Preston Wake (Michigan State University) - Tame derivatives and the Eisenstein ideal (abstract) 2019-2020 Seminars for the rest of the year cancelled due to university-wide suspension of non-essential events during coronavirus outbreak. 11/25/2019 - Jiakun Pan (TAMU) - Quantum Unique Equidistribution conjecture for Eisenstein series in the level aspect (abstract) 11/18/2019 - Rizwanur Khan (University of Mississippi) - Non-vanishing of Dirichlet L-functions (abstract) 11/4/2019 - Michał Zydor (University of Michigan) - On the Global Gan-Gross-Prasad conjecture for unitary groups (abstract) 2018-2019 06/17/2019 - (Joint seminar with ring theory) Sudesh K. Khanduja (IISER Mohali) - A walk through integrally closed domains and their applications in Number Theory (abstract) 04/29/2019 - Jay Jorgenson (CCNY) - Construction of non-holomorphic Eisenstein-type series and their Kronecker limit formulas (abstract) 04/17/2019 - (Wednesday 4:15--5:15, Joint seminar with representation theory) Joachim Schwermer (Universität Wien) - On the general linear group over arithmetic orders, related automorphic representations and corresponding cohomology groups (abstract) 04/15/2019 - Alia Hamieh (University of Northern British Columbia) - Value-Distribution of Cubic Hecke $L$-functions (abstract) 02/25/2019 - Harald Helfgott (Gottingen and CNRS) - Summing $\mu(n)$: a better elementary algorithm (abstract) 01/28/2019 - Lola Thompson (Oberlin) - Counting quaternion algebras with applications to spectral geometry (abstract) 01/14/2019 - Gene Kopp (Bristol) - From Hilbert's 12th problem to complex equiangular lines (abstract) 11/05/2018 - Keshav Aggarwal (OSU) - Application of trivial delta method towards subconvexity (abstract) 10/22/2018 - Elad Zelingher (Yale University) - Exterior square gamma factors for cuspidal representations of $\mathrm{GL}_n$ (abstract) 10/15/2018 - Nicolae Anghel (University of North Texas) - Heron Triangles with Constant Area and Perimeter (abstract) 10/08/2018 - Rongqing Ye (OSU) - Rankin--Selberg gamma factors of level zero representations of $GL_n$ (abstract) 09/17/2018 - Bill Mance (Adam Mickiewicz University) - Normal numbers with respect to the Cantor series expansions and possible applications to studying algebraic varieties (abstract) 2017-2018 03/19/2018 - Andrew Obus (UVA) - Reduction of dynatomic curves: The good, the bad, and the irreducible (abstract) 03/05/2018 - Qing Zhang (Sun Yat-Sen University) - Local converse theorem for unitary groups (abstract) 02/26/2018 - Joseph Vandehey (OSU) - Ergodicity of geometrically complete Iwasawa continued fractions (abstract) 01/29/2018 - Edmund Karasiewicz (UC Santa Cruz) - The Fourier Coefficients of a Minimal Parabolic Eisenstein Series on the Double Cover of GL(3) over Q (abstract) 11/27/2017 - Yeongseong Jo (OSU) - The local exterior square L-function for GL(n) (abstract) 11/20/2017 - Bob Hough (Stony Brook) - The shape of cubic and quartic fields (abstract) 11/13/2017 (3pm in MW154) - Claire Burrin (Rutgers) - Dedekind sums for cofinite Fuchsian groups (abstract) 10/23/2017 - Keshav Aggarwal (OSU) - Hybrid subconvex bound for certain Hecke character L-functions (abstract) 10/16/2017 - Yongxiao Lin (OSU) - Bounds for twists of $\rm GL(3)$ $L$-functions (abstract) 10/09/2017 - Shenhui Liu (University of Toronto) - Central L-values of Maass wave forms (abstract) 10/02/2017 - Roman Holowinsky (OSU) - Subconvexity for twists of automorphic L-functions without the delta method (abstract) 2016-2017 06/01/2017 (Thursday 12.40pm in MW154) - Paul Nelson (ETH Zurich) - Subconvex equidistribution of cusp forms (abstract) 04/24/2017 - Baiying Liu (Purdue) - On the local converse theorem for GL$_n$ (abstract) 04/17/2017 - Bao V. Le Hung (U Chicago) - Congruences between automorphic forms (abstract) 04/03/2017 - Liyang Zhang (Yale University) - Quantum Unique Ergodicity of Degenerate Eisenstein Series on GL(n) (abstract) 03/06/2017 - Kęstutis Česnavičius (UC Berkeley) - The Manin constant in the semistable case (abstract) 02/27/2017 - Jay Jorgenson (CCNY) - Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series (abstract) 02/20/2017 - Chen Wan (UMN) - Multiplicity one theorem for the Ginzburg-Rallis model (abstract) 02/13/2017 - Ralf Schmidt (Univ. of Oklahoma) - The paramodular conjecture and the representation theory of GSp(4) (abstract) 01/30/2017 - Brad Rodgers (Univ. Michigan) - Sums in short intervals and decompositions of arithmetic functions (abstract) 01/23/2017 - Eric Katz (OSU) - Tropical geometry and torsion point bounds (abstract) 10/10/2016 - Shenhui Liu (OSU) - Central L-derivative values of automorphic forms (abstract) 09/26/2016 - Joseph Vandehey (OSU) - When multiplying by $2$ is a hard thing to do (abstract) 2015-2016 04/25/2016 - Riad Masri (Texas A&M) - Singular moduli and the distribution of partition ranks (abstract) 04/18/2016 - Jonathan Bober (Bristol) - Computing modular forms (abstract) 04/14/2016 (Thursday 4.30pm in MW154) - Hongze Li (Shanghai Jiao Tong University) - Small gaps between the Piatetski-Shapiro primes (abstract) 04/04/2016 - Pankaj Vishe (Durham) - Hasse principle for higher degree hypersurfaces (abstract) 03/28/2016 - Jack Buttcane (SUNY) - The Kuznetsov formula on GL(3) (abstract) 03/23/2016 (Wednesday 4.30pm in MW154)- Leo Goldmakher (Williams) - Characters and their nonresidues (abstract) 03/07/2016 - Aaron Pollack (Stanford) - The Spin $L$-function on GSp$(6)$ (abstract) 02/22/2016 - Padmavathi Srinivasan (MIT) - Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points (abstract) 02/15/2016 - Sheng-Chi Liu (WSU) - The distribution of integral points on homogeneous varieties (abstract) 01/25/2016 - Scott Ahlgren (UIUC) - Kloosterman sums and Maass cusp forms of half integral weight for the modular group (abstract) 11/23/2015 - Ali Altuğ (Columbia University) - Arthur-Selberg trace formula and related problems (abstract) 11/02/2015 - Jay Jorgenson (CCNY) - Recent results in the study of groups of moonshine-type (abstract) 09/21/2015 - Ahmad El-Guindy (Texas A&M University at Qatar) - On Power Eigensystems of Drinfeld-Goss Hecke eigenforms (abstract) 2014-2015 04/13/2015 - Baiying Liu (Utah) - On cuspidality of global Arthur packets of quasi-split classical groups (abstract) 03/30/2015 - Kate Petersen (FSU) - Equidistribution of Norm 1 elements in Number Fields (abstract) 03/24/2015 (Tuesday 4.30pm in CH240) - Guangshi Lü (Shandong University) - Average behaviour of certain arithmetic functions (abstract) 03/23/2015 - Nigel Pitt (Maine) - A cuspidal analogue of Titchmarsh's divisor problem (abstract) 03/09/2015 - Paul Pollack (UGA) - Two analytic problems on CM elliptic curves (abstract) 02/09/2015 - Wissam Raji (AUB) - Unimodularity of zeros of period polynomials of Hecke Eigenforms (abstract) 11/24/2014 - Dani Szpruch (Indiana) - The Langlands Shahidi method and the metaplectic exceptional representations (abstract) 11/10/2014 - Ian Whitehead (UMN) - Toward a Casselman-Shalika Formula for Metaplectic Kac-Moody Groups (abstract) 11/03/2014 - Eyal Kaplan (OSU) - The theta-period of a cuspidal automorphic representation of GL(n) (abstract) 10/27/2014 - Matthew Young (Texas A&M) - Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets (abstract) 10/20/2014 - Min Lee (Bristol) - Shifted multiple Dirichlet series and spectral moments of Rankin-Selberg L-functions (abstract) 10/13/2014 - Meng Zhang (OSU) - Some improvements on Waring-Goldbach problem for fourth powers with almost equal variables (abstract) 10/06/2014 - Sandro Bettin (CRM) - The twisted second moment of the Dirichlet L-functions (abstract) 2013-2014 04/21/2014 - Michael Rubinstein (Waterloo) - Moments of zeta functions associated to hyperelliptic curves (abstract) 04/07/2014 - Paul Bourgade (IAS and Harvard) - Strong Szegö's theorem for $L$ functions (abstract) 03/31/2014 - Adam Harper (Cambridge) - Sharp bounds for moments of the Riemann zeta function (abstract) 03/24/2014 - Steven J Miller (Williams College) - Closed-form moments in elliptic curve families and low-lying zeros (abstract) 03/17/2014 - Tim Browning (Bristol) - The arithmetic of large-dimensional varieties is easy (abstract) 02/24/2014 - Djordje Milićević (Bryn Mawr) - Sub-Weyl subconvexity and short p-adic exponential sums (abstract) 02/17/2014 - Micah Milinovich (Ole Miss) - Estimates for the zeros of the Riemann zeta-function via Fourier analysis (abstract) 02/10/2014 - Maksym Radziwill (IAS) - Some recent interactions between sieves and L-functions (abstract) 02/03/2014 - Joseph Vandehey (UGA) - The unexpected strength of continued fractions on the Heisenberg group (abstract) 01/08/2014 - Farrell Brumley (Paris 13) - Counting cusp forms by analytic conductor (abstract) 11/25/2013 - Rudy Perkins (OSU) - Interpolating evaluation characters and the Anderson generating function for the Carlitz module (abstract) 11/18/2013 - Wing Chung (Jonathan) Lam (OSU) - Second moment of the central values of the symmetric square L-functions (abstract) 11/04/2013 - Zhilin Ye (OSU) - The Second Moment of Rankin-Selberg L-function and Hybrid Subconvexity Bound (abstract) 10/14/2013 - Ghaith Hiary (OSU) - Detecting squarefree numbers (abstract) 10/07/2013 - Zhi Qi (OSU) - Hybrid subconvexity bound of $L(1/2, Sym^2 f \times g)$ (abstract) 09/23/2013 - Fan Zhou (OSU) - Sato-Tate Equidistribution of Satake Parameters of Maass Forms on PGL(N) (abstract) 2012-2013 04/23/2013 - Guillaume Ricotta (Bordeaux) - Fourier coefficients of GL(3) automorphic forms in arithmetic progressions (abstract) 04/08/2013 - Craig Franze (OSU) - An asymptotic expansion related to the Dickman function. (abstract) 04/01/2013 - Joachim Schwermer (Vienna) - On Lefschetz numbers and arithmetically defined hyperbolic 3-manifolds. (abstract) 02/25/2013 - Bruce Berndt (UIUC) - Unpublished Manuscripts Published with Ramanujan's Lost Notebook. (abstract) 02/04/2013 - Youness Lamzouri (York U) - Large Character Sums. (abstract) 01/14/2013 - Dimitris Koukoulopoulos (Montreal) - When the sieve works. (abstract) 12/03/2012 - Ghaith Hiary (Bristol) - Computing Dirichlet $L$-functions. (abstract) 11/19/2012 - Kevin Ford (UIUC) - Sets $S$ of primes with $p$ in $S$ and $q|(p-1)$ implying $q$ in $S$. (abstract) 10/22/2012 - Micah Milinovich (Ole Miss) - Simple zeros of L-functions of modular forms. (abstract) 10/01/2012 - Tim All (OSU) - On p-adic annihilators of real ideal classes. (abstract) 09/24/2012 - David Goss (OSU) - From Carlitz's module to Euler's Gamma function. (abstract) 09/17/2012 - Roman Holowinsky (OSU) - Hybrid Subconvexity Bounds for Rankin-Selberg Convolutions. (abstract) We will consider various moment averages over special values of Rankin-Selberg convolution $L$-functions $L(\frac{1}{2}, \pi_1 \times \pi_2)$. Each $\pi_j$ will contribute to the size of the associated analytic conductor and we shall take advantage of this fact in order to obtain hybrid subconvexity bounds for individual $L$-values. Topics presented here will be a combination of ongoing joint projects with Nicolas Templier and Ritabrata Munshi. 09/10/2012 - Jim Cogdell (OSU) - The local Langlands correspondence for GL(n) and the symmetric and exterior square $\varepsilon$-factors (abstract) 2011-2012 05/21/2012 - Sun Kim (OSU) - Bessel function series and the circle and divisor problems. (abstract) In approximately 1915, Ramanujan recorded without proofs two identities involving doubly infinite series of Bessel functions. The two identities are connected with the classical circle and divisor problems, respectively. For each of Ramanujan's identities, there are three possible interpretations for the double series. The first identity was proved under those three and the second identity was proved under two of them. In this talk, we briefly review some key aspects of the proofs. Furthermore, we discuss trigonometric analogues of the identities, and a generalization of the first identity in the setting of Riesz sums. This is joint work with Bruce Berndt and Alexandru Zaharescu. 04/30/2012 - Ben Brubaker (MIT) - Demazure operators and Iwahori Whittaker functions. (abstract) Around 1980, Casselman and Shalika gave an elegant proof of a formula (conjectured by Langlands) for the spherical Whittaker function of an unramified principal series. We will begin by reviewing these terms and some key aspects of the proof, which relies on clever manipulations in the Iwahori-Hecke algebra. Then we explore similar formulas for Iwahori-fixed vectors in the unramified principal series, where we "rediscover" a Hecke algebra action due to Lusztig, in the context of equivariant K-theory. (This is joint work with Dan Bump and Tony Licata). 04/23/2012 - Hourong Qin (Nanjing) - The Local $L$-series of CM Elliptic Curves and Quadratic Polynomials Represent Primes. (abstract) Let $E$ be an elliptic curve defined over $\mathbb{Q}$ with complex multiplication. Fix an integer $r$. We give sufficient and necessary conditions for $a_p=r$ for some prime $p$. We show that there are infinitely many primes $p$ such that $a_p=r$ for some fixed integer $r$ if and only if a quadratic polynomial represents infinitely many primes $p$. In particular, for $E: y^2=x^3+x$, our result inplies that there are infinitely many primes $p$ such that $a_p=2$ if and only if there are infinitely many primes $p$ of the form $n^2+1$. 04/16/2012 - Peng Zhao (Princeton) - The Quantum Variance of PSL(2,Z)\PSL(2,R). (abstract) We discuss the quantum variance, which is introduced by Zelditch and describes the fluctuations of a quantum observable, on the phase space of modular surface. We asymptotically evaluate the quantum variance and show that it is equal to the classical variance of the geodesic flow on the phase space after inserting the "correction factor" of certain L-function's central value on each irreducible subspace. It is also very close to the arithmetic variance studied by Luo, Rudnick and Sarnak. This talk is based on a joint work with Peter Sarnak. 03/12/2012 - Henry Kim (Toronto) - Application of the strong Artin conjecture to the class number problem. (abstract) 02/09/2012 - Guillaume Ricotta (Bordeaux) - Height of Heegner points. (abstract) 12/05/2011 - Nathan Conrad Jones (University of Mississippi) - An alternative view of primitivity of Dirichlet characters. (abstract) 10/18/2011 (1:30 pm) - Amy DeCelles (Goshen) - Number theoretic applications of the automorphic spectral theory of higher rank groups. (abstract) 10/10/2011 - Federico Pellarin (St. Etienne) - On the values of certain L-series at even" positive integers. (abstract) 10/03/2011 - Kenneth Ward (Oklahoma State) - An asymptotic relation of class number and genus for abelian extensions of a function field. (abstract) 09/19/2011 - Abhishek Saha (ETH) - Determination of modular forms by Fourier coefficients. (abstract) 2010-2011 05/16/2011 - Sheng-Chi Liu (Texas A&M) - The L^2 restriction norms of Satio-Kurokawa lifts. (abstract) 05/09/2011 - Solomon Friedberg (Boston College) - Eisenstein series, crystals and ice. (abstract) 05/02/2011 - Ling Long (Iowa State) - Recent developments on modular forms for noncongruence subgroups. (abstract) 02/28/2011 - Jeff Hoffstein (Brown) - Shifted multiple Dirichlet series and moments of L-series. (abstract) 02/21/2011 - Gautam Chinta (CUNY) - Orthogonal periods of Eisenstein series. (abstract) 12/03/2010 - Noam Elkies (Harvard) - On the areas of rational triangles. (abstract) 11/22/2010 - Aaron Levin (Michigan State) - Runge's effective method for integral points. (abstract) 11/16/2010 - Lenny Taelman (Leiden) - The Carlitz sheaf, cyclotomic function fields, and Vandiver's conjecture. (abstract) 11/15/2010 - Xiaoqing Li (SUNY Buffalo) - The L^2 restriction of a GL(3) Maass form to GL(2). (abstract) 11/08/2010 - Paul Nelson (Caltech) - Equidistribution of cusp forms in the level aspect. (abstract) 11/01/2010 - Eddie Herman (AIM) - Beyond Endoscopy for the Asai L-function and Quadratic Base Change. (abstract) 10/25/2010 - David Goss (OSU) - The class number formula of Lenny Taelman. (abstract) 10/18/2010 - Jim Cogdell (OSU) - On Local L-functions. (abstract) 10/11/2010 - Yangbo Ye (Iowa) - Resonance of automorphic forms for GL(2) and GL(3). (abstract) 10/04/2010 - Timothy All (OSU) - Mihailescu's Theorem (formerly Catalan's conjecture); an outline of the proof. (abstract) More Number Theory