Calendar

I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.

Zoom: https://harvard.zoom.us/j/977347126

SARS-CoV-2 etiological pathogen of COVID-19 has resulted in a pandemic. There remains an urgent need of innovative technology of developing rapid diagnosis of active infections and affordable antiviral precise medicine for therapeutics. Most viruses have repetitive surface antigen units laid out on the virions following specific patterns forming the viral capsid or envelop. To develop precise instant diagnosis of active SARS-CoV-2 infections and novel antiviral candidates against SARS-CoV-2 infection and transmission we exploited the structural characteristics of viral surface proteins that can be matched at nanoscale precision by engineered DNA nanostructure platforms. Our preliminary data demonstrated that these pattern-matching DNA nanostructures can enable specific and sensitive sensing of SARS-CoV-2 viruses and have sufficient antiviral activities against SARS-CoV-2 pseudoviral and live viral infections. Our method can be transferrable to develop rapid diagnosis and precise inhibition of other enveloped viruses such as influenza and HIV. We are seeking expert advice from the mathematical and computational community to help with optimization of the DNA-based nanostructures.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.

Zoom: https://harvard.zoom.us/j/977347126

The original Volume Conjecture of Kashaev-Murakami-Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials of a knot in S^3 and the hyperbolic volume of its complement. I will discuss two different directions that lead to generalizations of this conjecture. The first direction concerns different quantum invariants of knots, arising from the colored SU(n) (with the colored Jones polynomial corresponding to the case n=2). I will first display subtle relations between congruence relations, cyclotomic expansions and the original Volume Conjecture for the colored Jones polynomials of knots. I will then generalize this point of view to the colored SU(n) invariant of knots. Certain congruence relations for the colored SU(n) invariants, discovered in joint work with K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume Conjecture for these colored SU(n) invariants. If time permits, I will briefly discuss similar ideas for the Superpolynomials that arise in HOMFLY-PT homology.

Another direction for generalization involves the Witten-Reshetikhin-Turaev and the (modified) Turaev-Viro quantum invariants of 3-manifolds. In a joint work with T. Yang, I formulated a Volume Conjecture for the asymptotics of these 3-manifolds invariants evaluated at certain roots of unity, and numerically checked it for many examples. Interestingly, this conjecture uses roots of unity that are different from the one usually considered in literature. These 3-manifolds invariants are only polynomially large at the usual root of unity as the level of the representation approaches infinity, which is predicted by Witten’s Asymptotic Expansion Conjecture. True understanding of this new phenomenon requires new physical and geometric interpretations that go beyond the usual quantum Chern-Simons theory. Currently these new Volume Conjectures have been proved for many examples by various groups. However, like the original Volume Conjecture, a complete proof for general cases is still an open problem in this area. In a recent joint work with J. Murakami, I proved the asymptotic behavior of the quantum 6j-symbol evaluated at the unusual root of unity, which could explain the Volume Conjectures for the asymptotics of the Turaev-Viro invariants in general.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

https://harvard.zoom.us/j/977347126

We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.

https://harvard.zoom.us/j/977347126

**Please note the Special Time**

Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of  advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.

https://harvard.zoom.us/j/977347126

**Please note the Special Tim**

On August 24, 2021, the CMSA will host our seventh annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

The 2021 Big Data Conference will take place virtually.

You must register to attend. 

Register here.

Organizers:

Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University

Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business

Horng-Tzer Yau, Professor of Mathematics, Harvard University

Sergiy Verstyuk, CMSA, Harvard University

**CANCELLED**

bstract: TBA

https://harvard.zoom.us/j/977347126

The pentagram map was introduced by Schwartz as a dynamical system on polygons in the real projective plane. The map sends a polygon to the shape formed by intersecting certain diagonals. This simple operation turns out to define a discrete integrable system, meaning that it is birational to a translation on a family of abelian varieties. Soloviev proved this over the complex numbers in 2013. We extend the result to any algebraically closed field of characteristic not equal to 2, and discuss the implications for the dynamics of rational maps over finite fields.

On Zoom. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information