
Speaker:Title: Mathematics and Machine Learning ProgramVenue: CMSA Room G10Mathematics and Machine Learning Program Dates: September 3–November 1, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138 Directions to CMSA Machine learning and AI are increasingly important tools in all fields of research. Recent milestones in machine learning for mathematics include datadriven discovery of theorems in knot theory and representation theory, the discovery and proof of new singular solutions of the Euler equations, new counterexamples and lower bounds in graph theory, and more. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this, yet to be elucidated…. 

Speaker:Title: Mathematical Aspects of Scattering Amplitudes ProgramVenue: CMSA, 20 Garden St, G10Mathematical Aspects of Scattering Amplitudes Program To receive email updates and program announcements, visit this link to sign up for the CMSA Mathematical Aspects of Scattering Amplitudes Program mailing list. Dates: April 15 – May 24, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138 Organizers: Nima ArkaniHamed (Institute for Advanced Study) Marcus Spradlin (Brown University) Andrew Strominger (Harvard University) Anastasia Volovich (Brown University) Lauren Williams (Harvard University) Participants: Michael Borinsky, ETH Zurich Jacob Bourjaily, Pennsylvania State University Ruth Britto, Trinity College Jordan Cotler, Harvard University Lance Dixon, Stanford Linear Accelerator Center James Drummond, University of Southampton Henriette Elvang, University of Michigan Chaim EvenZohar, Technion Livia Ferro, University of Hertfordshire Carolina Figueiredo, Princeton University Hadleigh Frost, Oxford University Bruno Gimenez, University… 

Speaker:Title: Arithmetic Quantum Field Theory ProgramVenue: CMSA Room G10Arithmetic Quantum Field Theory Program To receive email updates and program announcements, visit this link to sign up for the CMSA Arithmetic Quantum Field Theory Program mailing list. Dates: Feb. 5–Mar. 29, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 Directions to CMSA Organizers: David BenZvi (University of Texas Austin) Solomon Friedberg (Boston College) Natalie Paquette (University of Washington Seattle) Brian Williams (Boston University) This program will feature a weekly seminar series, workshops, and a conference. The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and Lfunctions. On one hand, there has… 

Speaker:Title: 2022 Summer Introduction to Mathematical ResearchVenue: virtualThe Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description: Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department) In this course, we will start with an introduction to computer programming, algorithms, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, and differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus… 

Speaker:Title: General Relativity ProgramVenue: CMSA Room G10During the Spring 2022 semester, the CMSA hosted a program on General Relativity. This semesterlong program included four minicourses, a conference, and a workshop. General Relativity Mincourses: March–May, 2022 General Relativity Conference: April 4–8, 2022 General Relativity Workshop: May 2–5, 2022 Program Visitors Dan Lee, CMSA/CUNY, 1/24/22 – 5/20/22 Stefan Czimek, Brown, 2/27/22 – 3/3/22 LanHsuan Huang, University of Connecticut, 3/13/22 – 3/19/222, 3/21/22 – 3/25/22, 4/17 /22– 4/23/22 MuTao Wang, Columbia, 3/21/22 – 3/25/22, 5/7/22 – 5/9/22 PoNing Chen, University of California, Riverside, 3/21/22 – 3/25/22, 5/7/22–5/9/22 Marnie Smith, Imperial College London, 3/27/22 – 4/11/22 Christopher Stith, University of Michigan, 3/27/22 – 4/23/22 Martin Taylor, Imperial College London, 3/27/22 – 4/11/22 Marcelo Disconzi, Vanderbilt, 5/9/22… 

Speaker:Title: SIMONS COLLABORATION ON HOMOLOGICAL MIRROR SYMMETRYVenue: VirtualThe Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or LandauGinzburg model). We envision that our goal of proving HMS in full generality can be accomplished by… 

Speaker:Title: Nonlinear Equations ProgramVenue: VirtualMost physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations. The subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date, it is an active field with recent exciting discoveries and renewed interests, and several long standing problems seem to be within reach. The special year aims… 

Speaker:Title: MATHPHYSICS PROGRAMVenue: VirtualIn the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum manybody theory. String theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as… 

Speaker:Title: GAMES ON HETEROGENEOUS GRAPHSVenue: VirtualA major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis. Here is a list of the scholars participating in this program. Name ShingTung Yau Martin Nowak Ben Adlam Ben Allen YuTing Chen An… 

Speaker:Title: CONDENSED MATTER PROGRAMVenue: VirtualThe methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using… 

Speaker:Title: Swampland ProgramVenue: VirtualPlease visit the Swampland Initiative for current events. The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity. During the 20212022 academic year, the CMSA hosted a program on the socalled “Swampland.” The Swampland program aims to determine which lowenergy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics… 

Speaker:Title: 2021 Summer Introduction to Mathematical ResearchVenue: VirtualThe Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description: Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department) In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint…. 

Speaker:Title: RANDOM MATRIX PROGRAMVenue: Virtualarge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of WignerDysonMehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix… 

Speaker:Title: TOPOLOGICAL ASPECTS OF CONDENSED MATTERVenue: VirtualDuring Academic year 201819, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines. As part of the Program, the CMSA will be hosting two workshops: Workshop on Topology and Quantum Phases of Matter (August 2728, 2018) Workshop on Topological Aspects of Condensed Matter (Septmeber 1011, 2019) . Additionally, a weekly Topology… 

Speaker:Title: THE SIMONS COLLABORATION IN HOMOLOGICAL MIRROR SYMMETRYVenue: VirtualThe Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves… 

Speaker:Title: Mathematical BiologyVenue: VirtualDuring Academic year 201819, the CMSA will be hosting a Program on Mathematical Biology. Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen… 

Speaker:Title: SPACETIME AND QUANTUM MECHANICS, TOTAL POSITIVITY AND MOTIVESVenue: VirtualRecent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 2030 participants. They will also invite 1020 longerterm visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10. Organizers: Nima ArkaniHamed (IAS) Lauren Williams (Harvard) Alexander Postnikov (MIT) Thomas Lam (Michigan) . Workshops: Spacetime and Quantum Mechanics Workshop, October 2830, 2019 Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or… 