## FRG Grad SeminarThis is the webpage for the grad seminar of the focused research group on averages of \(L\)-functions and arithmetic stratification funded by the NSF grant DMS-1854398, centered at the American Institute of Mathematics. This is an online seminar aimed at graduate students in the FRG, though non-grad students often attend. It is meant for blackboard-style expository talks; typically, past speakers have either given an overview of a general field or went over influential papers with a focus on techniques they find useful and wanted to advertise. If you would like to volunteer to give a talk, or you would like to attend the seminar, please send me an email. For the schedule as well as notes and recordings of past talks, please see below. ## Upcoming Talks## No Talks (Summer Break)## Past Talks## Spring 2023## [05-Jun-2023] Emily Quesada-Herrera (TU Graz)“On the vertical distribution of the zeros of the Riemann zeta-function” (notes, video) ## [29-May-2023] Jaime Hernandez Palacios (Mississippi)“Gaps between zeros of zeta and L-functions of high degree” (notes) ## [22-May-2023] Igor Shparlinski (UNSW)“Bilinear forms with Kloosterman and Salié Sums and Moments of L-functions” (notes, video) ## [15-May-2023] Vorappan (Fai) Chandee (Kansas State)“The eighth moment of \(\Gamma_1(q)\) L-functions” (notes, video) ## [08-May-2023] Alessandro Fazzari (AIM)“Averages of long Dirichlet polynomials with modular coefficients” (notes, video) ## [01-May-2023] Kiseok Yeon (Purdue)“The Hasse principle for random projective hypersurfaces via the circle method” (notes, video) ## [24-Apr-2023] Eun Hye Lee (Stony Brook)“The Shintani Zeta Functions” (notes, video) ## [17-Apr-2023] Matilde Lalín (Montréal)“The distribution of values of cubic \(L\)-functions at \(s=1\)” (notes, video) ## [10-Apr-2023] Aleksander Simonič (UNSW Canberra)“Some conditional estimates for functions in the Selberg class” (notes, video) ## [20-Mar-2023] Peter Zenz (Brown)“On the Distribution of Holomorphic Cusp Forms and Applications” (notes, video) ## [13-Mar-2023] Ian Whitehead (Swarthmore)“Multiple Dirichlet Series and Moments of L-functions” (video) ## [10-Mar-2023] Ofir Gorodetsky (Oxford)“How many smooth numbers and smooth polynomials are there?” (notes, video) ## [27-Feb-2023] Xiannan Li (Kansas State)“Quadratic Twists of Modular L-functions” (notes, video) ## [20-Feb-2023] Katy Woo (Princeton)“Small scale distribution of primes in four-term arithmetic progressions” (notes, video) ## [13-Feb-2023] Rizwanur Khan (Mississippi)“The fourth moment of Dirichlet L-functions and related problems” (notes, video) ## [06-Feb-2023] Keshav Aggarwal (Rényi Institute)“Bound for the existence of prime gap graphs” (notes, video) ## [30-Jan-2023] David Farmer (AIM)“The zeta function when it is particularly large” (notes, video) ## [23-Jan-2023] Nathan Ng (Lethbridge)“The eighth moment of the Riemann zeta function” (notes, video) ## Fall 2022## [19-Dec-2022] George Dickinson (Manchester)“Second moments of Dirichlet L-functions” (notes, video) ## [12-Dec-2022] Alexander Dobner (Michigan)“Optimization and moment methods in number theory” (notes, video) ## [05-Dec-2022] Asif Zaman (Toronto)“Random multiplicative functions and a simplified model” ## [28-Nov-2022] Aled Walker (KCL)“Correlations of sieve weights and distributions of zeros” (notes, video) ## [21-Nov-2022] Alexander Dunn (Caltech)“Bias in cubic Gauss sums: Patterson's conjecture” (video) ## [14-Nov-2022] Jakob Streipel (Maine)“Using second moments to count zeros” (notes, video) ## [07-Nov-2022] Daodao Yang (TU Graz)“Large values of derivatives of the Riemann zeta function and related problems” (notes) ## [31-Oct-2022] Emma Bailey (CUNY)“Large values of \(\zeta\) on the critical line” (video) ## [17-Oct-2022] Dan Goldston (SJSU)“Small gaps and spacings between Riemann zeta-function zeros” (notes, video) ## [10-Oct-2022] Lasse Grimmelt (Oxford)“Primes in large arithmetic progressions and applications to additive problems” (notes, video) ## [03-Oct-2022] Louis Gaudet (Rutgers)“The least Euler prime via a sieve approach” (video) ## [26-Sep-2022] Hua Lin (UC Irvine)“One-level density of zeros of Dirichlet L-function over function fields” (notes, video) ## [22-Sep-2022] Caroline Turnage-Butterbaugh (Carleton)“Moments of Dirichlet L-functions” (notes) ## Spring 2022## [30-May-2022] Micah Milinovich (Mississippi)“Estimates for zeta and L-functions via Fourier optimization” (notes, video) ## [23-May-2022] Jori Merikoski (Oxford)“Primes in sparse polynomials sets” (notes, video) ## [16-May-2022] Martin Čech (Concordia)“Two ways to compute moments in the family of real Dirichlet L-functions” (notes, video) ## [02-May-2022] Alexandra Florea (UC Irvine)“Upper bounds for positive and negative moments of the Riemann zeta function” (notes, video) ## [25-Apr-2022] Kevin Hughes (Bristol)“A primer on Discrete Restriction Theory” (notes, video) ## [18-Apr-2022] Alia Hamieh (UNBC)“Distribution of values of logarithmic derivatives of L-functions” (notes, video) ## [11-Apr-2022] Ayla Gafni (Mississippi)“Uniform distribution and geometric incidence theory” (video) ## [04-Apr-2022] Victor Wang (Princeton)“Special subvarieties over finite and infinite fields” (notes, video) ## [28-Mar-2022] Joshua Stucky (Kansas State)“Smooth numbers in arithmetic progressions” (notes, video) ## [21-Mar-2022] Kunjakanan Nath (UIUC)“Primes with restricted digits” (notes, video) ## [14-Mar-2022] Ofir Gorodetsky (Oxford)“Chebyshev's bias for primes and for sums of two squares” (notes, video) ## [07-Mar-2022] Vivian Kuperberg (Stanford)“The Hardy–Littlewood \(k\)-tuple conjecture and intervals with many primes” (notes, video) ## [28-Feb-2022] Peter Humphries (Virginia)“Spectral reciprocity and applications” (notes, video) ## [14-Feb-2022] Siegfred Baluyot (AIM)“The shifted convolution of divisor functions” (notes, video) ## Fall 2021## [13-Dec-2021] Brad Rodgers (Queen's)“Averages of products and ratios of L-functions and characteristic polynomials” (video) ## [29-Nov-2021] Chung-Hang (Kevin) Kwan (Columbia)“Some aspects of \(\Gamma\)-functions” (notes, video) ## [22-Nov-2021] Fan Ge (William & Mary)“Critical points of the Riemann zeta-function” (notes, video) ## [15-Nov-2021] Fatma Çiçek (IIT Gandhinagar)“Value distribution of the Riemann zeta-function on the half-line” (notes, video) ## [08-Nov-2021] Emilia Alvarez (Bristol)“Random matrices and Painlevé equations” (video) ## [02-Nov-2021] Shehzad Hathi (UNSW Canberra)“The LLL algorithm and its applications to Mertens conjecture” (notes, video) ## [25-Oct-2021] Max Xu (Stanford)“Limiting distributions of sums of random multiplicative functions” (notes, video) ## [11-Oct-2021] Louis Gaudet (Rutgers)“The Kloosterman Circle Method” (notes, video) ## [04-Oct-2021] Caroline Turnage-Butterbaugh (Carleton)“Gaps between zeros of the Riemann zeta-function” (notes, video) ## Spring 2021## [21-Jun-2021] Akshat Mudgal (Bristol/Purdue)“An introduction to Vinogradov’s mean value theorem” (notes, video) ## [14-Jun-2021] Amita Malik (AIM/Max Planck)“Equidistribution of \(\alpha p^{\theta}\) with a Chebotarev condition and applications to extremal primes” (video) ## [07-Jun-2021] Winston Heap (Shandong)“Mean values of long Euler products” (notes, video) ## [17-May-2021] Jared Duker Lichtman (Oxford)“The Riemann hypothesis for curves” (notes, video) ## [19-Apr-2021] Vivian Kuperberg (Stanford)“The second moment of quadratic twists of modular L-functions (after Soundararajan and Young)” (notes, video) ## [12-Apr-2021] Ofir Gorodetsky (Oxford)“The variance of the sum of an arithmetic function over random short intervals” (notes, video) ## [08-Mar-2021] Max Xu (Stanford)“Distribution and moments of random multiplicative functions” (notes, video) ## [22-Feb-2021] Chung-Hang (Kevin) Kwan (Columbia)“Averages of Fourier coefficients” (notes, video) ## [15-Feb-2021] Quanli Shen (Lethbridge)“The first moment of quadratic twists of modular L-functions” (notes, video) ## [08-Feb-2021] Emilia Alvarez (Bristol)“An overview of random matrix theory for number theorists” (notes, video) ## [01-Feb-2021] Alessandro Fazzari (Genova)“A survey on the central limit theorem for the Riemann zeta function” (notes, video) |