This volume contains the proceedings of IDPEIS-22: Isomonodromic Deformations, Painleve Equations, and Integrable Systems, held virtually June 27-July 1, 2022, hosted by Columbia University, and AGMPS-22: Algebraic Geometry, Mathematical Physics, and Solitons, held October 7-9, 2022, at Columbia University, New York, NY. This volume is dedicated to the legacy of Igor Krichever, and the papers in it are closely connected to the main themes of Igor's research interests. The range of topics in this volume is very broad. The paper by Bobenko, Bobenko, and Suris generalizes Krichever's approach to algebro-geometric integrability to the dimer models. The paper by Rohrle and Zakharov considers a tropical version of classical algebro-geometric objects such as the Prym variety. The papers by Grekov and Nekrasov and by Felder, Smirnov, Tarasov, and Varchenko study quantum integrable systems from the point of view of 3D mirror symmetry and gauge theories. The paper by Etingof and Varchenko studies properties of certain families of flat connections, and the paper by Yamada describes a Lax form of a quantum $q$-Painleve equation. The paper by Cherednik belongs to the area of combinatorial probability and the paper by Braverman and Kazhdan to the geometric Langlands program. The two remaining papers are in the area of applied mathematics. The paper by de Leon, Frauendiener, and Klein considers the computational approach to the Schotky problem. The paper by Blackstone, Gassot, and Miller studies soliton ensembles for the Benjamin-Ono equation.
Mikhail Bershtein, The University of Edinburgh, Edinburgh, UK. Anton Dzhamay, BIMSA, Beijing, People's Republic of China. Andrei Okounkov, Columbia University, New York, NY
Chapters; Chapter 1. Sieve questions; Chapter 2. Elementary considerations on arithmetic functions; Chapter 3. Bombieri's sieve; Chapter 4. Sieve of Eratosthenes-Legendre; Chapter 5. Sieve principles and terminology; Chapter 6. Brun's sieve-The big bang; Chapter 7. Selberg's sieve-Kvadrater er positive; Chapter 8. Sieving by many residue classes; Chapter 9. The large sieve; Chapter 10. Molecular structure of sieve weights; Chapter 11. The beta-sieve; Chapter 12. The linear sieve; Chapter 13. Applications to linear sequences; Chapter 14. The semi-linear sieve; Chapter 15. Applications-Choice but not prime; Chapter 16. Asymptotic sieve and the parity principle; Chapter 17. Combinatorial identities; Chapter 18. Asymptotic sieve for primes; Chapter 19. Equidistribution of quadratic roots; Chapter 20. Marching over Gaussian primes; Chapter 21. Primes represented by polynomials; Chapter 22. Level of distribution of arithmetic sequences; Chapter 23. Primes in short intervals; Chapter 24. The least prime in an arithmetic progression; Chapter 25. Almost-prime sieve; Appendix A. Mean values of arithmetic functions; Appendix B. Differential-difference equations
