Calendar
- 07April 7, 2023
Current Developments in Mathematics 2023
1 Oxford Street, Cambridge, MA 02138 USACurrent Developments in Mathematics 2023
April 7-8, 2023
Harvard University Science Center
Lecture Hall C
Speakers:
Amol Aggarwal – Columbia University (Columbia)Bhargav Bhatt – Institute for Advanced Study, Princeton University, & University of Michigan (IAS/Princeton/UMichigan)Paul Bourgade – New York University, Courant Institute (NYU Courant)Vesselin Dimitrov – Institute for Advanced Study & Georgia Institute of Technology (IAS/Georgia Tech)Greta Panova – University of Southern California (USC)REQUESTS FOR FUNDING ARE CLOSED AS OF MARCH 10TH, 2023.
Conference Schedule
Download PDF for a detailed schedule of lectures and events.
Friday, April 7
Saturday, April 8
- 1:30 p.m. – 2:20 p.m. Part 1
- 2:20 p.m. – 2:30 p.m. Break
2:30 p.m. – 3:20 p.m. Part 2
Bhargav Bhatt
$p$-adic motives
- 9:05 a.m. – 9:55 a.m. Part 1
- 9:55 a.m. – 10:05 a.m. Break
10:05 a.m. – 10:55 a.m. Part 2
Greta Panova
Computational complexity in algebraic combinatorics
3:20 p.m. – 3:35 p.m.
Break
10:55 a.m. – 11:10 a.m.
Break
- 3:35 p.m. – 4:25 p.m. Part 1
- 4:25 p.m. – 4:35 p.m. Break
4:35 p.m. – 5:25 p.m. Part 2
Amol Aggarwal
Universality results in random tiling models
- 11:10 a.m. – 12 p.m. Part 1
- 12 p.m. – 1:30 p.m. Lunch
1:30 p.m. – 2:20 p.m. Part 2
Paul Bourgade
Random matrices, the Riemann zeta function and branching processes
2:20 p.m. – 2:35 p.m.
Break
- 2:35 p.m. – 3:25 p.m. Part 1
- 3:25 p.m. – 3:35 p.m. Break
3:35 p.m. – 4:25 p.m. Part 2
Vesselin Dimitrov
Modular forms and arithmetic algebraization methods
Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau
Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology.
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CMSA Quantum Matter in Mathematics and Physics: Enhancing Detection of Topological Order by Local Error Correction
20 Garden Street, Cambridge, MA 02138The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.
This seminar offers the option to attend by Zoom. For information on how to join, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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https://forms.gle/1ewa7KeP6BxBuBeRA Gauge Theory and Topology Seminar: Instantons on Joyce's G2-manifolds
1 Oxford Street, Cambridge, MA 02138 USAAs 7-manifolds with special holonomy, examples of compact G2-manifolds were first constructed by Joyce as resolutions of flat G2-orbifolds. Later Walpuski constructed non-trivial G2-instantons over Joyce’s manifolds via gluing techniques. In this talk, I will first explain how to define a deformation invariant of G2-orbifolds by counting flat connections, then describe the moduli space of instantons over certain non-compact G2-manifolds that appeared in Joyce’s construction, with the aim to give a complete description of moduli spaces over some examples in Joyce’s list.