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1  2  3  4  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Harmonic analysis of 2d CFT partition functions
10:30 AM12:00 PM August 4, 2021 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
 5  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Designer DNAbased nanoconstructs in viral detection and blocking
9:00 AM10:00 AM August 5, 2021 SARSCoV2 etiological pathogen of COVID19 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 SARSCoV2 infections and novel antiviral candidates against SARSCoV2 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 patternmatching DNA nanostructures can enable specific and sensitive sensing of SARSCoV2 viruses and have sufficient antiviral activities against SARSCoV2 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 DNAbased nanostructures. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Unnuclear physics: conformal symmetry in nuclear reactions
10:30 AM12:00 PM August 5, 2021 I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “unnucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in highenergy 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 unnuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in shortdistance reactions at the LHC. Zoom: https://harvard.zoom.us/j/977347126
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8  9  10  11  CMSA EVENT: CMSA Strongly Correlated Quantum Materials and HighTemperature Superconductors Seminar: Order Fractionalization*
10:30 AM12:00 PM August 11, 2021 I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of offdiagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the YaoLeeKitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an orderfractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done with Yashar Komijani, Anna Toth, Premi Chandra and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
 12  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Recent Progress on Volume Conjectures of links as well as 3manifolds
9:00 AM10:00 AM August 12, 2021 The original Volume Conjecture of KashaevMurakamiMurakami 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 HOMFLYPT homology. Another direction for generalization involves the WittenReshetikhinTuraev and the (modified) TuraevViro quantum invariants of 3manifolds. In a joint work with T. Yang, I formulated a Volume Conjecture for the asymptotics of these 3manifolds 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 3manifolds 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 ChernSimons 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 6jsymbol evaluated at the unusual root of unity, which could explain the Volume Conjectures for the asymptotics of the TuraevViro invariants in general. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: On the firewall puzzle
10:30 AM12:00 PM August 12, 2021 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 stateindependent 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
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22  23  24  CMSA EVENT: Big Data Conference 2021
All day August 24, 2021 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: ShingTung Yau, William Caspar Graustein Professor of Mathematics, Harvard University Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business HorngTzer Yau, Professor of Mathematics, Harvard University Sergiy Verstyuk, CMSA, Harvard University
 25  26  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: **CANCELLED**
10:30 AM12:00 PM August 26, 2021  ALGEBRAIC DYNAMICS SEMINAR
3:00 PM5:00 PM August 26, 2021 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
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