# Mathematical Sciences Research Institute

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1. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:34 PM PDT
2. # SeminarTea for DDC Members and Participants

Updated on Sep 24, 2020 01:39 PM PDT
3. # SeminarDDC - Junior Seminar

Updated on Aug 28, 2020 03:04 PM PDT
4. # SeminarRAS - Minicourse

Updated on Sep 24, 2020 02:18 PM PDT
5. # SeminarTea for RAS Members and Participants

Updated on Sep 16, 2020 10:10 AM PDT
6. # SeminarTea for DDC Members and Participants

Updated on Sep 24, 2020 01:39 PM PDT
7. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
8. # SeminarDDC/RAS - Career Development Seminar: Superpower Theory

Updated on Sep 23, 2020 11:24 AM PDT
9. # SeminarDDC - Valuation Theory: Deeply ramified fields and their relatives

Updated on Sep 23, 2020 09:04 AM PDT
10. # SeminarRAS - Minicourse

Updated on Sep 24, 2020 03:49 PM PDT
11. # SeminarDDC - Definability seminar: What is existentially definable in between $\Q$ and $\Z$?

Updated on Sep 24, 2020 02:10 PM PDT
12. # SeminarTea for RAS Members and Participants

Updated on Sep 16, 2020 10:10 AM PDT
13. # SeminarRAS - Minicourse

Updated on Sep 24, 2020 03:43 PM PDT
14. # SeminarTea for DDC Members and Participants

Updated on Sep 24, 2020 01:39 PM PDT
15. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:10 AM PDT
16. # SeminarDDC Online Seminar: (Z,+) has a Borel complete reduct

Updated on Sep 24, 2020 09:19 AM PDT
17. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
18. # SeminarTea for DDC Members and Participants

Updated on Sep 24, 2020 01:39 PM PDT
19. # SeminarDDC-Minicourse: Applying Topology to Spaces of Countable Structures

Updated on Sep 09, 2020 09:06 AM PDT
20. # SeminarFellowship of the Ring, National Seminar: Tropical ideals

Updated on Sep 24, 2020 11:48 AM PDT
21. # SeminarRAS - This week I am thinking about...

Updated on Sep 24, 2020 11:58 AM PDT
22. # SeminarDDC - Computability Theory: Generically computable structures

Updated on Sep 24, 2020 09:35 AM PDT
23. # SeminarRAS - Minicourse

Updated on Sep 24, 2020 04:06 PM PDT
24. # SeminarTea for RAS Members and Participants

Updated on Sep 16, 2020 10:10 AM PDT
25. # SeminarTea for DDC Members and Participants

Updated on Sep 24, 2020 01:39 PM PDT
26. # SeminarRAS - Minicourse

Updated on Sep 24, 2020 04:03 PM PDT
27. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:35 PM PDT
28. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 17, 2020 09:24 AM PDT
29. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 17, 2020 09:24 AM PDT
30. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:04 PM PDT
31. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
32. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:34 AM PDT
33. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:22 PM PDT
34. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:10 AM PDT
35. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:32 AM PDT
36. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
37. # SeminarDDC-Minicourse: Applying Topology to Spaces of Countable Structures

Updated on Sep 09, 2020 09:07 AM PDT
38. # SeminarFellowship of the Ring, National Seminar: Grothendieck's localization problem

Updated on Sep 24, 2020 11:50 AM PDT
39. # SeminarRAS - This week I am thinking about...

Updated on Sep 24, 2020 11:58 AM PDT
40. # SeminarDDC Online Seminar

Updated on Aug 12, 2020 04:45 PM PDT
41. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:37 PM PDT
42. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 17, 2020 09:26 AM PDT
43. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 17, 2020 09:26 AM PDT
44. # SeminarDDC Junior Seminar

Updated on Sep 09, 2020 03:54 PM PDT
45. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
46. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:34 AM PDT
47. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:22 PM PDT
48. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:10 AM PDT
49. # SeminarDDC Online Seminar

Updated on Aug 31, 2020 11:21 AM PDT
50. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
51. # SeminarDDC-Minicourse: Applying Topology to Spaces of Countable Structures

Updated on Sep 09, 2020 09:07 AM PDT
52. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
53. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:32 AM PDT
54. # Workshop2020 SACNAS – The National Diversity in STEM Conference

The largest multidisciplinary and multicultural STEM diversity event in the country, the SACNAS conference serves to equip, empower, and energize participants for their academic and professional paths in STEM.

Updated on Sep 17, 2020 12:18 PM PDT
55. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:38 PM PDT
56. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:22 AM PDT
57. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
58. # SeminarDDC Junior Seminar

Updated on Sep 09, 2020 03:55 PM PDT
59. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
60. # SeminarRAS - Mini Course

Updated on Sep 24, 2020 10:02 AM PDT
61. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:34 AM PDT
62. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:23 PM PDT
63. # SeminarRAS - Mini Course

Updated on Sep 24, 2020 10:02 AM PDT
64. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
65. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:32 AM PDT
66. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
67. # SeminarRAS - Mini Course

Updated on Sep 24, 2020 10:02 AM PDT
68. # SeminarDDC-Minicourse: Applying Topology to Spaces of Countable Structures

Updated on Sep 09, 2020 09:07 AM PDT
69. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
70. # SeminarDDC Online Seminar

Updated on Aug 12, 2020 04:46 PM PDT
71. # SeminarRAS/DDC - Career Development Panel

Updated on Sep 23, 2020 02:31 PM PDT
72. # SeminarRAS/DDC - Career Development Panel: Tea

Updated on Sep 23, 2020 03:19 PM PDT
73. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:39 PM PDT
74. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:22 AM PDT
75. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
76. # SeminarDDC Junior Seminar

Updated on Sep 09, 2020 03:55 PM PDT
77. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
78. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:34 AM PDT
79. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:24 PM PDT
80. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
81. # SeminarDDC Online Seminar

Updated on Sep 10, 2020 11:54 AM PDT
82. # SeminarRAS Postdoc Seminar

Updated on Sep 24, 2020 11:12 AM PDT
83. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
84. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:32 AM PDT
85. # SeminarRAS/DDC - Career Development Panel

Updated on Sep 23, 2020 03:13 PM PDT
86. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:39 PM PDT
87. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:22 AM PDT
88. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
89. # SeminarDDC Junior Seminar

Updated on Sep 09, 2020 03:56 PM PDT
90. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
91. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:34 AM PDT
92. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:24 PM PDT
93. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
94. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:32 AM PDT
95. # SeminarRAS Postdoc Seminar

Updated on Sep 24, 2020 11:13 AM PDT
96. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
97. # SeminarDDC - Online Seminar

Updated on Aug 24, 2020 04:22 PM PDT
98. # SeminarRAS/DDC - Career Development Panel with Murray Cantor

Updated on Sep 23, 2020 03:14 PM PDT
99. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:40 PM PDT
100. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:22 AM PDT
101. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
102. # SeminarDDC Junior Seminar

Updated on Sep 09, 2020 03:56 PM PDT
103. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
104. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:35 AM PDT
105. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:25 PM PDT
106. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
107. # SeminarDDC Online Seminar

Updated on Aug 31, 2020 11:21 AM PDT
108. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
109. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
110. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:34 AM PDT
111. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:41 PM PDT
112. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:22 AM PDT
113. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
114. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:06 PM PDT
115. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
116. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:35 AM PDT
117. # SeminarDefinability seminar

Updated on Aug 28, 2020 03:25 PM PDT
118. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
119. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:34 AM PDT
120. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
121. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
122. # SeminarDDC Online Seminar

Updated on Aug 12, 2020 04:49 PM PDT
123. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:42 PM PDT
124. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:21 AM PDT
125. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
126. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:06 PM PDT
127. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
128. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:35 AM PDT
129. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:25 PM PDT
130. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:42 PM PDT
131. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:21 AM PDT
132. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
133. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:07 PM PDT
134. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
135. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:35 AM PDT
136. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:25 PM PDT
137. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
138. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:34 AM PDT
139. # SeminarRAS Postdoc Seminar

Updated on Sep 24, 2020 11:15 AM PDT
140. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
141. # SeminarDDC Online Seminar

Updated on Aug 12, 2020 04:51 PM PDT
142. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:42 PM PDT
143. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 11, 2020 09:21 AM PDT
144. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 10, 2020 10:19 AM PDT
145. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:10 PM PDT
146. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
147. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:36 AM PDT
148. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:25 PM PDT
149. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
150. # SeminarDDC Online Seminar

Updated on Aug 31, 2020 11:19 AM PDT
151. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
152. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
153. # SeminarDDC - Computability Theory

Updated on Aug 31, 2020 11:35 AM PDT
154. # SeminarDDC - Diophantine Problems

Updated on Aug 24, 2020 03:43 PM PDT
155. # SeminarRAS - Research Seminar (Part 1)

Updated on Sep 18, 2020 03:45 PM PDT
156. # SeminarRAS - Research Seminar (Part 2)

Updated on Sep 18, 2020 03:45 PM PDT
157. # SeminarDDC Junior Seminar

Updated on Aug 28, 2020 03:11 PM PDT
158. # SeminarRAS - PA Seminar

Created on Aug 28, 2020 02:23 PM PDT
159. # SeminarDDC - Valuation Theory

Updated on Aug 31, 2020 09:36 AM PDT
160. # SeminarDDC - Definability seminar

Updated on Aug 28, 2020 03:26 PM PDT
161. # SeminarDDC-Reading Group: Valuations on dp-finite fields

Updated on Sep 09, 2020 09:11 AM PDT
162. # SeminarRAS Postdoc Seminar

Updated on Aug 24, 2020 11:17 AM PDT
163. # SeminarFellowship of the Ring, National Seminar:

Updated on Sep 03, 2020 11:07 AM PDT
164. # SeminarDDC Online Seminar

Updated on Aug 12, 2020 04:52 PM PDT
165. # ProgramMathematical problems in fluid dynamics

Organizers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Centre National de la Recherche Scientifique (CNRS); Institut de Mathématiques de Jussieu), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)

Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.

The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the well-known Euler equations for inviscid fluids, and the Navier-Stokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.

Updated on Apr 25, 2019 02:32 PM PDT
166. # WorkshopConnections Workshop: Mathematical problems in fluid dynamics

Organizers: Hajer Bahouri (Centre National de la Recherche Scientifique (CNRS); Institut de Mathématiques de Jussieu), Juhi Jang (University of Southern California), LEAD Anna Mazzucato (Pennsylvania State University), Sijue Wu (University of Michigan)
Image by Noomann Bassou

This workshop will feature talks by prominent female mathematicians whose research lies in and interfaces with mathematical fluids featuring water waves,  free boundaries, fluid structures,  viscous fluids and turbulence. The talks will be appropriate for graduate students, post-docs, and researchers in areas above mentioned. There will also be a panel discussion and a contributed poster session. This workshop is open to all mathematicians.

Updated on Feb 20, 2020 11:31 AM PST
167. # WorkshopIntroductory Workshop: Mathematical problems in fluid dynamics

Organizers: Nicolas Burq (Université de Paris XI), Anne-Laure Dalibard (Université de Paris VI (Pierre et Marie Curie)), Jean Marc Delort (Université de Paris XIII (Paris-Nord)), LEAD Mihaela Ifrim (University of Wisconsin-Madison), Irena Lasiecka (University of Memphis), Vladimir Sverak (University of Minnesota Twin Cities)

The workshop will address topics in the PDE analysis of the basic equations of the incompressible fluid dynamics (the Euler equations for inviscid flows, the Navier Stokes equations for viscous flows), interface problems (water waves), and other related equations. Open problems and connections to related branches of mathematics will be discussed, including the phenomena of turbulence and the zero viscosity limit. Both theoretical and numerical aspects of these topics will be considered. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

Updated on Nov 25, 2019 01:09 PM PST
168. # WorkshopRecent Developments in Fluid Dynamics

Organizers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Centre National de la Recherche Scientifique (CNRS); Institut de Mathématiques de Jussieu), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)
Water waves

The aim of the workshop is to bring together a broad array of researchers working on incompressible fluid dynamics. Some of the key topics to be covered are Euler flows, Navier Stokes equations as well as water wave flows and associated model equations. Some emphasis will also be placed on numerical analysis of the above evolutions.

Updated on Jun 18, 2019 09:54 AM PDT
169. # WorkshopCritical Issues in Mathematics Education 2021: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors

Organizers: Naneh Apkarian (Arizona State University), David Bressoud (Macalester College), Pamela Burdman (Just Equations), Jamylle Carter (Diablo Valley college), Ted Coe (Northwest Evaluation Association), Estrella Johnson (Virginia Polytechnic Institute and State University), W. Gary Martin (Auburn University), Michael O'Sullivan (San Diego State University), William Penuel (University of Colorado), LEAD Chris Rasmussen (San Diego State University), Daniel Reinholz (San Diego State University), Wendy Smith (University of Nebraska), David Webb (University of Colorado)

The world is changing, along with perceptions. Many call for the improvement of mathematics teaching and learning, for both citizenry and STEM preparation. To achieve sustainable change, though, the focus needs to extend from individuals to systems. It is not enough to change one classroom or one course. Transformation requires change at all levels: in teaching, programmatic practices, and institutions. This workshop will bring together teachers and researchers from universities, community colleges, and K-12 schools to explore the reasons for and processes by which change in university mathematics departments is initiated, promoted, and sustained and lessons learned from change efforts in K-12. It will review what we know about change at all levels and reflect on stories of failure and success.

Updated on Sep 11, 2020 01:00 PM PDT
170. # WorkshopHot Topics: Topological Insights in Neuroscience

Organizers: Carina Curto (Pennsylvania State University), Chad Giusti (University of Delaware), LEAD Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL)), Ran Levi (University of Aberdeen)
Image created by Nicolas Antille, of the visualization team of the Blue Brain Project at EPFL

The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

Updated on Jun 25, 2020 03:57 PM PDT
171. # Summer Graduate School2021 CRM-PIMS Summer School in Probability (CRM, Montreal)

Organizers: LEAD Louigi Addario-Berry (McGill University), Omer Angel (University of British Columbia), Alexander Fribergh (University of Montreal), Mathav Murugan (University of British Columbia), Edwin Perkins (University of British Columbia)
The Sherrington-Kirkpatrick model, aka the randomly-weighted complete graph. Edge weights are indicated using grayscale. Six distinguished vertices have been randomly chosen; edges between those vertices are shaded black to form a "hidden signal".

The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

The phrase "group dynamics" is used loosely here -- it may refer to species migration, the spread of a virus, or the propagation of electrons through an inhomogeneous medium, to name a few examples. Very commonly, such systems can be described via stochastic processes which approximately behave like the solution of an appropriate partial differential equation in the large-population limit.

Updated on Aug 31, 2020 10:40 AM PDT
172. # Summer Research in Mathematics2021 Summer Research in Mathematics

Due to the pandemic, the 2019 Summer Research in Mathematics program was postponed to 2020.  Therefore, MSRI is not accepting new applications at this time.

MSRI's Summer Research in Mathematics program provides space, funding, and the opportunity for in-person collaboration to small groups of mathematicians, especially women and gender-expansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI aims to mitigate the obstacles faced by these groups, improve the odds of research project completion, and deepen their research experience.

The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

Updated on Aug 31, 2020 11:43 AM PDT
173. # Summer Graduate SchoolSparsity of Algebraic Points

Organizers: Philipp Habegger (University of Basel), LEAD Hector Pasten (Pontificia Universidad Católica de Chile)
The Corvaja-Zannier proof of Siegel's theorem using subspaces. Illustrated by Sofía Pastén Vásquez.

The theory of Diophantine equations is understood today as the study of algebraic points in algebraic varieties, and it is often the case that algebraic points of arithmetic relevance are expected to be sparse.

This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

Updated on Sep 15, 2020 04:26 PM PDT
174. # Summer Graduate SchoolMathematics of Big Data: Sketching and (Multi-) Linear Algebra

Organizers: LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center)

This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

Updated on Aug 04, 2020 09:38 AM PDT
175. # Summer Graduate SchoolFoundations and Frontiers of Probabilistic Proofs (Zurich, Switzerland)

Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)
Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

Updated on Aug 04, 2020 09:47 AM PDT
176. # Summer Graduate SchoolMetric Geometry and Geometric Analysis (Oxford, United Kingdom)

Organizers: LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)

The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.

Updated on Aug 04, 2020 10:05 AM PDT
177. # Summer Graduate SchoolGauge Theory in Geometry and Topology

Organizers: Lynn Heller (Universität Hannover), Francesco Lin (Columbia University), LEAD Laura Starkston (University of California, Davis), Boyu Zhang (Princeton University)
Image by Nick Schmitt

Figure 1. A rotationally symmetric solution to the self-duality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3-space visualized by the wireframe.

Gauge theory is a geometric language used to formulate many fundamental physical phenomena, which has also had profound impact on our understanding of topology. The main idea is to study the space of solutions to partial differential equations admitting a very large group of local symmetries. Starting in the late 1970s, mathematicians began to unravel surprising connections between gauge theory and many aspects of geometric analysis, algebraic geometry and low-dimensional topology. This influence of gauge theory in geometry and topology is pervasive nowadays, and new developments continue to emerge.

The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.

Updated on Aug 04, 2020 10:04 AM PDT
178. # Summer Graduate SchoolRandom Conformal Geometry

Organizers: Mario Bonk (University of California, Los Angeles), Steffen Rohde (University of Washington), LEAD Fredrik Viklund (Royal Institute of Technology)
a random quasiconformal map obtained from Beltrami equation by randomly assigning the values of +-1/2 for the Beltrami coefficient on small squares subdividing the unit square

This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semester-long program  "The Analysis and Geometry of Random Spaces".  Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.

Updated on Aug 04, 2020 10:24 AM PDT
179. # Summer Graduate SchoolRecent Topics in Well Posedness (Taipei, Taiwan)

Organizers: Jungkai Chen (National Taiwan University), Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

Updated on Jul 20, 2020 10:01 AM PDT
180. # ProgramUniversality and Integrability in Random Matrix Theory and Interacting Particle Systems

Organizers: LEAD Ivan Corwin (Columbia University), Percy Deift (New York University, Courant Institute), Ioana Dumitriu (University of California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University-Purdue University Indianapolis), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)

The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models. This program seeks to reinforce and expand the fruitful interaction at the interface of these areas, as well as to showcase some of the important developments and applications of the past decade.

Updated on Apr 20, 2020 11:12 AM PDT
181. # WorkshopConnections Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems

Organizers: LEAD Ioana Dumitriu (University of California, San Diego), Alisa Knizel (Columbia University)
An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

This workshop will focus on cutting-edge research in random matrices and integrable probability. We will explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers. We will have a panel discussion of topics relevant to junior researchers, women, and minorities; a poster session for students and recent PhDs; and other social events. This workshop is open to and welcomes all mathematicians.

Updated on May 06, 2020 11:42 AM PDT
182. # WorkshopIntroductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems

Organizers: LEAD Gerard Ben Arous (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon), Sylvia Serfaty (New York University, Courant Institute), Horng-Tzer Yau (Harvard University)

The introductory workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Updated on Mar 19, 2020 11:30 AM PDT
183. # WorkshopRegularity Theory for Minimal Surfaces and Mean Curvature Flow

Organizers: LEAD Christine Breiner (Fordham University), Otis Chodosh (Stanford University), Luca Spolaor (University of California, San Diego), Lu Wang (California Institute of Technology)

This workshop will explore connections between the regularity theory of minimal surfaces and of mean curvature flow. Recent breakthroughs have improved our understanding of singularity formation in both settings but the current research trends are becoming increasingly disparate. Experts from both areas will present their research and there will be ample free time to establish connections between the topics.

Updated on Sep 14, 2020 09:32 AM PDT
184. # WorkshopIntegrable structures in random matrix theory and beyond

Organizers: LEAD Jinho Baik (University of Michigan), Alexei Borodin (Massachusetts Institute of Technology), Tamara Grava (University of Bristol; International School for Advanced Studies (SISSA/ISAS)), Alexander Its (Indiana University-Purdue University Indianapolis), Sandrine Péché (Université de Paris VII (Denis Diderot))
Image by Alexei Borodin.

This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.

Updated on Jul 31, 2019 03:22 PM PDT
185. # ProgramThe Analysis and Geometry of Random Spaces

Organizers: LEAD Mario Bonk (University of California, Los Angeles), Joan Lind (University of Tennessee), Steffen Rohde (University of Washington), Eero Saksman (University of Helsinki), Fredrik Viklund (Royal Institute of Technology), Jang-Mei Wu (University of Illinois at Urbana-Champaign)

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers,  random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Updated on Nov 20, 2019 02:12 PM PST
186. # ProgramComplex Dynamics: from special families to natural generalizations in one and several variables

Organizers: LEAD Sarah Koch (University of Michigan), Jasmin Raissy (Institut de Mathématiques de Toulouse), Dierk Schleicher (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)
The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere.

Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond.

Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.

Updated on Nov 20, 2019 02:12 PM PST
187. # ProgramFloer Homotopy Theory

Organizers: Mohammed Abouzaid (Columbia University), Andrew Blumberg (University of Texas, Austin), Kristen Hendricks (Rutgers University), Robert Lipshitz (University of Oregon), LEAD Ciprian Manolescu (Stanford University), Nathalie Wahl (University of Copenhagen)
Illustrated by Nathalie Wahl

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes.  In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.

Updated on Nov 25, 2019 01:27 PM PST
188. # ProgramAnalytic and Geometric Aspects of Gauge Theory

Organizers: Laura Fredrickson (Stanford University), Rafe Mazzeo (Stanford University), Tomasz Mrowka (Massachusetts Institute of Technology), Laura Schaposnik (University of Illinois at Chicago), LEAD Thomas Walpuski (Humboldt-Universität)

The mathematics and physics around gauge theory have, since their first interaction in the mid 1970’s, prompted tremendous developments in both mathematics and physics.  Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories.  This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology.  Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications.  The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.

Updated on Feb 05, 2020 10:22 AM PST
189. # ProgramAlgebraic Cycles, L-Values, and Euler Systems

Organizers: Henri Darmon (McGill University), Ellen Eischen (University of Oregon), LEAD Benjamin Howard (Boston College), David Loeffler (University of Warwick), Christopher Skinner (Princeton University), Sarah Zerbes (University College London), Wei Zhang (Massachusetts Institute of Technology)
Some Gaussian periods for the 255,255-th cyclotomic extension. Image credit: E. Eischen, based on earlier work by W. Duke, S. R. Garcia, T. Hyde, and R. Lutz

The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups.

The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations.

The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles.

Updated on Feb 25, 2020 11:41 AM PST