#### RG Analysis and Partial Differential Equations

#### Summer term 2021

## S4B1 - Graduate Seminar on Analysis

### Analytic Approaches to the Riemann Hypothesis

### Instructors

Dr. Felipe Gonçalves, PD Dr. Pavel Zorin-Kranich.

### Dates

- Tuesday, 8:15 - 10:00
- Preliminary meeting: Th, 2021-02-11, 16:00
- First meeting at a different time: Mo, 2021-04-12, 14:15 - 16:00

### Topics

Topics that are not marked with (taken) are available.- Lagarias, Jeffrey C. - An elementary problem equivalent to the Riemann hypothesis. Amer. Math. Monthly 109 (2002), no. 6, 534–543. (taken)
- Barrett, Wayne W.; Forcade, Rodney W.; Pollington, Andrew D. - On the spectral radius of a (0,1) matrix related to Mertens' function. Proceedings of the Victoria Conference on Combinatorial Matrix Analysis (Victoria, BC, 1987). Linear Algebra Appl. 107 (1988), 151–159. Note: student should explain a little bit about why sum(j=1,n,mu(n)) << n^(1/2+epi) is equivalent to RH. (taken)
- Levinson, Norman - More than one third of zeros of Riemann's zeta-function are on σ=1/2 Advances in Math. 13 (1974), 383–436. Note: Simpler and more accessible expositions given by Young [MR2745463] and Bombieri [MR0444585]. Note: Comment that Conrey has the best result essentially: 40%. (taken)
- Beurling-Nyman Criterion Chapter 3 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents. see also: https://www.esi.ac.at/static/esiprpr/esi623.pdf
- Rodgers, Brad; Tao, Terence - The de Bruijn–Newman constant is non-negative. Forum Math. Pi 8 (2020), e6, 62 pp. 2 students. See chapter 5 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents for more background. (taken)
- Integral Equations Chapter 8 of Kevin Broughan - Equivalents of the Riemann Hypothesis II Analytic Equivalents. 8.1-8.4 (not 8.5)
- Michael Griffin, Ken Ono, Larry Rolen, Don Zagier - Jensen polynomials for the Riemann zeta function and other sequences (taken)

### Dates

- April 12: Felipe
- April 20: Topic 1
- April 27: 2
- May 4: 3
- May 11: 4
- May 18: 5
- June 1: 5
- June 15: 7 - canceled
- June 22: 8
- July 6: 6

### Talk preparation

Contact Felipe to discuss your topic at least a week before your presentation date.## News

Prof. Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts

Hirzebruch lecture by Rahul Pandharipande on Monday, May 15, 2023

Lucas Mann recevices the Hausdorff memorial award 2021/22

Bachelor Prize 2021/22 of the BMG awarded

Prof. Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019

Prof. Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Rajula Srivastava receives Association for Women in Mathematics Dissertation Prize

Prof. Ana Caraiani wins a New Horizons in Mathematics Prizes 2023

Pius XI Medal awarded to Professor Peter Scholze

Prof. Valentin Blomer und Prof. Georg Oberdieck erhalten ERC grants

Grants for Mathematics students from Ukraine

Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Prof. Peter Scholze elected as Foreign Member of the Royal Society

Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz

Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant