Calendar
- 13March 13, 2022No events
- 14March 14, 2022No events
- 15March 15, 2022
CMSA Combinatorics, Physics and Probability: Moduli space of tropical curves, graph Laplacians and physics.
I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
CMSA Algebraic Geometry in String Theory: 2-categorical 3d mirror symmetry
It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
Joint Harvard-CUHK-YMSC Differential Geometry Seminar: Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable
billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.
Zoom Link: https://cuhk.zoom.us/j/97001510671
(Meeting ID: 970 0151 0671; Passcode: 20220316)
- 16March 16, 2022
Quantum Matter in Mathematics and Physics: Summing Over Bordisms In 2d TQFT
Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
- 17March 17, 2022
CMSA Interdisciplinary Science: On optimization and generalization in deep learning
Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
CMSA Interdisciplinary Science: On optimization and generalization in deep learning
Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
Quantum Matter in Mathematics and Physics: A Hike through the Swampland
The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
- 18March 18, 2022
Current Developments in Mathematics 2021-22
Current Developments in Mathematics 2021-22
March 18-19, 2022
Harvard University Science Center
Lecture Hall B
Speakers:
Jessica Fintzen (University of Cambridge and Duke University)
Ryan O’Donnell (Carnegie Mellon)
Jack Thorne (University of Cambridge)
Cynthia Vinzant (University of Washington)
Mu-Tao Wang (Columbia)This conference will also be available in hybrid format as an online Zoom Webinar. To attend virtually, please register using the Zoom Registration links for each day of the conference. Separate Zoom registrations are required for Friday’s and Saturday’s sessions.
Because of COVID protocols, advance registration is required and capacity may be restricted. If you’d like to participate, please fill out the registration form below by March 16.
Register HereLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to cdm@math.harvard.edu. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research.
Schedule
• Friday, March 18, 2022
• Friday Zoom Webinar Registration
• Jessica Fintzen
1:30-2:20pm I: Representations of p-adic groups
2:30-3:20pm II: Representations of p-adic groups• Mu-Tao Wang
3:35-4:25pm I: Angular momentum and supertranslation in general relativity
4:35-5:25pm II: Angular momentum and supertranslation in general relativity• Saturday, March 19, 2022
• Saturday Zoom Webinar Registration
• Jack Thorne
9:05-9:55am I: L-functions and symmetric power functoriality
10:05-10:55am II: L-functions and symmetric power functoriality• Ryan O’Donnell
11:10am-12:00pm I: Learning and Testing Quantum States
12:00-1:30pm Lunch
1:30-2:20pm II: Learning and Testing Quantum States• Cynthia Vinzant
2:35-3:25pm I: Log-concavity in matroids and expanders
3:40-4:35pm II: Log-concavity in matroids and expandersOrganizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard)
Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.
- 19March 19, 2022
Current Developments in Mathematics 2021-22
Current Developments in Mathematics 2021-22
March 18-19, 2022
Harvard University Science Center
Lecture Hall B
Speakers:
Jessica Fintzen (University of Cambridge and Duke University)
Ryan O’Donnell (Carnegie Mellon)
Jack Thorne (University of Cambridge)
Cynthia Vinzant (University of Washington)
Mu-Tao Wang (Columbia)This conference will also be available in hybrid format as an online Zoom Webinar. To attend virtually, please register using the Zoom Registration links for each day of the conference. Separate Zoom registrations are required for Friday’s and Saturday’s sessions.
Because of COVID protocols, advance registration is required and capacity may be restricted. If you’d like to participate, please fill out the registration form below by March 16.
Register HereLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to cdm@math.harvard.edu. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research.
Schedule
• Friday, March 18, 2022
• Friday Zoom Webinar Registration
• Jessica Fintzen
1:30-2:20pm I: Representations of p-adic groups
2:30-3:20pm II: Representations of p-adic groups• Mu-Tao Wang
3:35-4:25pm I: Angular momentum and supertranslation in general relativity
4:35-5:25pm II: Angular momentum and supertranslation in general relativity• Saturday, March 19, 2022
• Saturday Zoom Webinar Registration
• Jack Thorne
9:05-9:55am I: L-functions and symmetric power functoriality
10:05-10:55am II: L-functions and symmetric power functoriality• Ryan O’Donnell
11:10am-12:00pm I: Learning and Testing Quantum States
12:00-1:30pm Lunch
1:30-2:20pm II: Learning and Testing Quantum States• Cynthia Vinzant
2:35-3:25pm I: Log-concavity in matroids and expanders
3:40-4:35pm II: Log-concavity in matroids and expandersOrganizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard)
Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.