news

See Older News

announcements

See Older Announcements

upcoming events

  • September 21, 2021
    3:00 pm
    Science Center 507

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    Speaker: Christopher Eur - Harvard University   Title: Tautological classes of matroids
< 2021 >
August
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
1
2
3
4
5
6
7
8
9
10
11
  • CMSA EVENT: CMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Seminar: Order Fractionalization*
    10:30 AM-12:00 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 off-diagonal 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 Yao-Lee-Kitaev 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
    order-fractionalized 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 3-manifolds
    9:00 AM-10:00 AM
    August 12, 2021

    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)

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: On the firewall puzzle
    10:30 AM-12:00 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 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

13
14
15
16
17
18
19
20
21
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:

    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

25
26
27
28
29
30
31
September
September
September
September