news

See Older News

announcements

Diving Into Math with Emmy Noether
September 10, 2022      4:30 pm
Diving Into Math with Emmy Noether A theatre performance about the life of one of history’s most influential mathematicians. When: Saturday, September 10, 2022 Panel...
Read more
See Older Announcements

upcoming events

< 2021 >
November
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
October
1
2
3
4
  • CMSA EVENT: CMSA Interdisciplinary Science Seminar: Exploring Invertibility in Image Processing and Restoration
    9:00 AM-10:00 AM
    November 4, 2021

    Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.


    Zoom ID: 950 2372 5230 (Password: cmsa)

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Fusion Category Symmetries in Quantum Field Theory
    10:30 AM-12:00 PM
    November 4, 2021

    Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

  • ALGEBRAIC DYNAMICS SEMINAR
    4:00 PM-6:00 PM
    November 4, 2021

    I will speak about recent joint work with Bell, Diller, and Jonsson in which we refute a conjecture of Bellon-Viallet by constructing (mostly) explicit examples of birational maps of projective 3-space with transcendental dynamical degree, also known as algebraic entropy.  The set of possible dynamical degrees for birational maps of projective space is known to be a countable set, with nearly all examples given by eigenvalues of integer matrices (and thus algebraic), yet we demonstrate the existence of infinitely many transcendental values in this set.  The proof builds on previous work of Bell-Diller-Jonsson, combining the study of monomial maps of toric varieties with classical techniques from Diophantine approximation.


    for more information, go to:

5
6
7
8
9
10
  • DIFFERENTIAL GEOMETRY SEMINAR
    3:00 AM-4:00 AM
    November 10, 2021

    will speak on:

    Higher rank DT theory from rank 1


    Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

    ********************************************************************

    For details visit:

    http://www.ims.cuhk.edu.hk/cgi-bin/SeminarAdmin/bin/Web

    http://www.ims.cuhk.edu.hk/activities/seminar/joint-dg-seminar/

    **Please note time is HONG KONG TIME** (3 am EST)

  • CMSA EVENT: CMSA Colloquium: Hypergraph decompositions and their applications
    9:30 AM-10:30 AM
    November 10, 2021

    Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary `divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.


    Zoom link: https://harvard.zoom.us/j/95767170359 (Password: cmsa)

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT
    10:00 AM-11:30 AM
    November 10, 2021

    *Note special time*

    It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.

    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    November 10, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    A phenomenon underlying many remarkable results in number theory is the natural Galois action on the cohomology of symplectic groups of integers. In joint work with Soren Galatius and Akshay Venkatesh, we define a symplectic variant of algebraic K-theory, which carries a natural Galois action for similar reasons. We compute this Galois action and characterize it in terms of a universality property, in the spirit of the Langlands philosophy.

11
12
13
14
15
16
17
  • CMSA EVENT: CMSA Colloquium: Curve counting on surfaces and topological strings
    9:30 AM-10:30 AM
    November 17, 2021

    Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X,D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X,D), including the log Gromov–Witten invariants of the pair, the Gromov–Witten invariants of an associated higher dimensional Calabi–Yau variety, the open Gromov–Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar–Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    https://harvard.zoom.us/j/95767170359

    (Password: cmsa)

  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms.  Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated self-intersection.  We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet L-functions at integer points, and explain the connection with the arithmetic Siegel-Weil conjecture of Kudla-Rapoport.  This is joint work with Jan Bruinier.

  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms.  Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated self-intersection.  We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet L-functions at integer points, and explain the connection with the arithmetic Siegel-Weil conjecture of Kudla-Rapoport.  This is joint work with Jan Bruinier.

  • SEMINARS
    4:00 PM-5:00 PM
    November 17, 2021

    will speak on:

    Quantum cohomology as a deformation of symplectic cohomology


    Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.


    Zoom Link: https://cuhk.zoom.us/j/94377988344

    Meeting ID: 943 7798 8344
    Passcode: 20211117

  • OPEN NEIGHBORHOOD SEMINAR
    4:30 PM-5:30 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    In several areas of mathematics, including probability theory, asymptotic functional analysis, statistics and data science, one is interested in high-dimensional objects, such as measures, data or convex bodies. One common theme is to try to understand what lower-dimensional projections can say about the corresponding high-dimensional objects. I will describe several results that address this question, starting with classical results and moving on to more recent breakthroughs, my own research and some open questions. The talk will be self-contained and accessible to undergraduate students.

    Website: https://people.math.harvard.edu/~ana/ons/

18
19
  • SEMINARS
    3:30 PM-4:30 PM
    November 19, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    will speak on:

    Extended weak order in affine type


    The extended weak order is a partial order associated to a Coxeter system (W,S). It is the containment order on “biclosed” sets of positive roots in the (real) root system associated to W. When W is finite, this order coincides with the (right) weak order on W, but when W is infinite, the weak order on W is a proper order ideal in the extended weak order. It is well-known that the weak order on W is a lattice if and only if W is finite. In contrast, it is a longstanding conjecture of Matthew Dyer that the extended weak order is a lattice for any W, which is open in the case that W is infinite. I will present joint work with David Speyer where we prove this conjecture for the affine Coxeter groups.

20
21
22
23
24
25
26
27
28
29
30
  • CMSA EVENT: CMSA Combinatorics, Probability and Physics Seminar: Resistance curvature – a new discrete curvature on graphs
    9:30 AM-10:30 AM
    November 30, 2021

    The last few decades has seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.
    Based on joint work with He Guo and Kalen Patton, see https://arxiv.org/abs/2011.09459   

     

December
December
December
December