news

See Older News

announcements

Current Developments in Mathematics 2024
April 5, 2024 - April 6, 2024     
Current Developments in Mathematics 2024 April 5-6, 2024 Harvard University Science Center Lecture Hall C Register Here   Speakers: Daniel Cristofaro-Gardiner - University of Maryland...
Read more
See Older Announcements

upcoming events

«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
February
February
February
February
February
1
2
3
4
  • CMSA EVENT: CMSA Colloquium: Strong bounds for arithmetic progressions

    Speaker: Raghu Meka – UCLA

    4:30 PM-5:30 PM
    March 4, 2024
    20 Garden Street, Cambridge, MA 02138

    Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., a 3-term arithmetic progression)?

    In 1953, Roth showed this is the case when C is roughly (log log N). Behrend in 1946 showed that C can be at most exp(sqrt(log N)). Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on C to C = (log N)^(1+c) for some constant c > 0.

    This talk will describe a new work showing that C can be much closer to Behrend’s construction. Based on joint work with Zander Kelley.

5
6
7
  • CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Geometric construction of toric NCRs

    Speaker: Jesse Huang – University of Alberta

    10:30 AM-11:30 AM
    March 7, 2024
    20 Garden Street, Cambridge, MA 02138

    The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk, I will survey these perspectives. The talk is based on joint works with P. Zhou, joint works with D. Favero, and work in progress with D. Favero.

     

    Zoom: https://harvard.zoom.us/j/93338480366?pwd=NEROWElhWStQVjVLRVZFSm1tV1ZCdz09
    Passcode: 564263

     

8
9
10
11
12
  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: The defect of a cubic fourfold

    Speaker: Lisa Marquand – New York University

    3:00 PM-4:00 PM
    March 12, 2024
    1 Oxford Street, Cambridge, MA 02138 USA
    The defect of a cubic threefold with isolated singularities is a measure of the failure of Poincare duality, and also the failure to be Q-factorial. From the work of Cheltsov, a cubic threefold with only nodal singularities is Q factorial if and only if there are at most 5 nodes. We investigate the defect of cubic threefolds with worse than nodal isolated singularities, and provide a geometric method to compute this global invariant. One can then compute the Mixed Hodge structure on the middle cohomology of the cubic threefold, in terms of the defect (a global invariant) and local invariants (Du Bois and Link invariants) determined by the singularity types. We then relate the defect to geometric properties of the cubic threefold, showing it is positive if and only if the cubic contains a plane or a rational normal cubic scroll. The focus of this work is to provide more insight into the existence of reducible fibers for compactified intermediate jacobian fibrations associated to a smooth (not necessarily general) cubic fourfold. This is joint work with Sasha Viktorova.

    For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar

13
14
15
16
17
18
  • CMSA EVENT: CMSA Colloquium: Koszul duality & twisted holography for asymptotically flat spacetimes

    Speaker: Natalie Paquette – University of Washington Seattle

    4:30 PM-5:30 PM
    March 18, 2024
    20 Garden Street, Cambridge, MA 02138

    Koszul duality has been understood in recent years to characterize order-type defects in twists of supersymmetric field theories. This notion has been generalized, from a physical point of view, by studying couplings between D-branes and closed string theories in the topological string. Computing the D-brane backreaction, and studying the resulting open/closed string duality, is the purview of the twisted holography program. Twisted holography seeks to study supersymmetric sectors of the AdS/CFT correspondence using these methods, and leverage the appropriate generalization of Koszul duality to elucidate the bulk/boundary map. When applying these methods to a topological string configuration on twistor space, one can construct an instance of twisted holography in which a 2d chiral algebra, supported on the “celestial sphere”, is dual to a 4d theory in an asymptotically flat spacetime. This is the first such top-down example of holography in a 4d asymptotically flat spacetime. This talk describes joint work done, variously, with Kevin Costello, Brian Williams, and Atul Sharma.

19
  • SEMINARS: Probability Seminar: Bipartite spherical spin glass at critical temperature (with a random matrix detour)

    Speaker: Elizabeth Collins-Woodfin – McGill University

    1:30 PM-2:30 PM
    March 19, 2024

    One of the fascinating phenomena of spin glasses is the dramatic change in behavior that occurs between the high and low temperature regimes. The free energy of the spherical Sherrington-Kirkpatrick (SSK) model, for example, has Gaussian fluctuations at high temperature, but Tracy-Widom fluctuations at low temperature. A similar phenomenon holds for the bipartite SSK model, and we show that, when the temperature is within a small window around the critical temperature, the free energy fluctuations converge to an independent sum of Gaussian and Tracy-Widom random variables (joint work with Han Le). Our work follows two recent papers that proved similar results for the SSK model (by Landon and by Johnstone, Klochkov, Onatski, Pavlyshyn). Analyzing bipartite SSK at critical temperature requires a variety of tools including classical random matrix results, contour integral techniques, and a CLT for the log-characteristic polynomial of Laguerre (Wishart) random matrices evaluated near the spectral edge. This last ingredient was not present in the literature when we began our project, so I will discuss our proof of this CLT, which has other applications separate from bipartite spin glasses.

    This seminar will take place on Zoom.

    Zoom link: https://harvard.zoom.us/j/98500892109

  • SEMINARS: Probability Seminar: Elizabeth Collins-Woodfin, McGill

    Speaker: Elizabeth Collins-Woodfin – McGill

    1:30 PM-2:30 PM
    March 19, 2024

    Abstract TBA

  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Extending the torelli map to alternative compactifications of the moduli space of curves

    Speaker: Changho Han – University of Waterloo

    3:00 PM-4:00 PM
    March 19, 2024
    1 Oxford Street, Cambridge, MA 02138 USA

    It is well-known that the Torelli map, that turns a smooth curve of genus g into its Jacobian (a principally polarized abelian variety of dimension g), extends to a map from the Deligne—Mumford moduli of stable curves to the moduli of semi-abelic varieties by Alexeev. Moreover, it is also known that the Torelli map does not extend over the alternative compactifications of the moduli of curves as described by the Hassett—Keel program, including the moduli of pseudostable curves (can have nodes and cusps but not elliptic tails). But it is not yet known whether the Torelli map extends over alternative compactifications of the moduli of curves described by Smyth; what about the moduli of curves of genus g with rational m-fold singularities, where m is a positive integer bounded above? As a joint work in progress with Jesse Kass and Matthew Satriano, I will describe moduli spaces of curves with m-fold singularities (with topological constraints) and describe how far the Torelli map extends over such spaces into the Alexeev compactifications.

    For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar

  • SEMINARS: Introductory Math Seminar: Can biocalculus help fix the calculus image problem?

    Speaker: Carrie Diaz Eaton – Bates

    3:00 PM-5:00 PM
    March 19, 2024

    Calculus has an image problem in the biology major. Students are anxious about taking it, due to prior personal experience and because calculus as a major gateway course contributes significantly to attrition in biology. Biology instructors are not seeing the desired gains in problem solving and graphical interpretation important for their courses. This is exacerbated by increasing interest in big data and computational skills rather than the proofs and algebraic techniques methods which have traditionally played a dominant role in calculus. “Biocalculus,” on the other hand, is a promising remedy for these issues. Students in biocalculus articulate more detailed connections to the theory of their disciplines, have increased retention, and much higher learning gains. Biocalculus leverages students’ passion and knowledge about biology and data in ways that may be particularly important to repaying educational debts to students with identities marginalized in STEM. However, significant challenges remain, particularly professional development and other investment needed to support such interdisciplinary courses and the epistemological consequences of the shift required.

20
21
  • CMSA EVENT: CMSA Active Matter Seminar: Decoding The Origins of Fluidity in Multicellular Systems

    Speaker: Max Bi – Northeastern University

    1:00 PM-2:00 PM
    March 21, 2024
    20 Garden Street, Cambridge, MA 02138

    Organisms continually adapt to mechanical forces at the cellular and tissue levels, a process crucial for sustaining vital life functions. In pivotal physiological processes, such as cancer progression and embryonic development, tissues are often poised near solid-like and fluid-like states. My talk will delve into three critical aspects of this phenomenon: (1) utilizing computational models that draw parallels with soft matter physics, we examine shear-induced rigidity and the origins of fluidity in epithelial tissues; (2) exploring the intricate relationship between external mechanical stresses and internal cellular dynamics, unraveling a range of rheological behaviors, such as shear thinning and thickening, which are key for understanding rheological responses in varying physical contexts; and (3) investigating how cellular processes like division and apoptosis influence tissue states, with a specific focus on the emergence of hexatic phases, an intermediate state exhibiting properties of both solids and liquids.


    This seminar will be held in person and on Zoom.

    https://harvard.zoom.us/j/96657833341

    Password: cmsa

22
  • HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: A Tropical Edrei theorem

    Speaker: Konstanze Rietsch – King’s College London

    4:15 PM-5:15 PM
    March 22, 2024

    The classical Edrei theorem from the 1950’s gives a parametrisation for infinite upper-triangular totally positive real Toeplitz matrices by pairs of sequences of positive real parameters with finite sum. These infinite matrices (and their parameters) are central for understanding characters of the infinite symmetric group, as was discovered by Thoma, who reproved Edrei’s theorem in the 1960’s. There is also a totally different (totally positive) theorem about Toeplitz matrices that relates to quantum cohomology of flag varieties and mirror symmetry [R,06]. Namely, this theorem provides an (inverse) parametrization in terms of ‘quantum parameters’ for the finite Toeplitz matrix case. This talk will be about new tropical versions of these parametrisation results. Toeplitz matrices in the tropical world turn out to have a nice combinatorial description. We also uncover a surprising relationship between the classical Edrei parameters and the quantum parameters of quantum cohomology. This work builds on results of Judd and Ludenbach and relates also to Lusztig’s parametrisation of his canonical basis.

    ===============================

    For more info, see https://math.mit.edu/combin/

23
24
25
26
27
28
29
30
31
April
April
April
April
April
April