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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...
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  • CMSA EVENT: CMSA Active Matter: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

    Speaker: Josef Käs – Leipzig University

    1:00 PM-2:00 PM
    September 6, 2022

    Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.
    Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.
    We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

    For more information on how to join, please see:

  • CMSA EVENT: Diving Into Math with Emmy Noether
    4:30 PM-6:30 PM
    September 10, 2022

    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 Discussion: 4:30 p.m. – 5 p.m. | Play: 5:15 p.m. | Reception: 6:30 p.m. – 7:30 p.m.

    Where: Harvard University Hilles Cinema, Student Organization Center at Hilles (SOCH)

    59 Shepard Street, Cambridge, MA 02138


    • Melissa Franklin | Harvard University Mallinckrodt Professor of Physics
    • Barry Mazur | Harvard University Gerhard Gade University Professor
    • Monica Noether | Vice President, Charles River Associates | Grandniece of Emmy Noether
    • David Rowe | Mainz University Professor


    Unfortunately, as of right now venue capacity has been reached. If you’d like to sign up to be waitlisted, please register below and we will inform you by Friday, September 9 if seats become available.

    Waitlist Registration

    Emmy Noether (1882-1935) was one of the most influential mathematicians of the last century. Her works and teachings left a lasting mark on modern algebra, opening new avenues for a modern structural perspective in mathematics.

    The ensemble Portraittheater Vienna (Austria) together with the Frei Universität Berlin (Germany) produced a biographical play about Emmy Noether, directed by Sandra Schüddekopf and starring Anita Zieher as Emmy. In September 2022, “Diving into Math with Emmy Noether” will tour the USA for the first time and play at several universities and colleges. The Harvard Department of Mathematics and the Center of Mathematical Sciences and Applications (CMSA) are proud to bring this performance to Harvard University.

    Based on historical documents and other sources, the script was written by Sandra Schüddekopf and Anita Zieher in cooperation with the historians Mechthild Koreuber and David E. Rowe. On stage and in videos, Emmy Noether’s fascinating personality comes alive in her reflections and conversations with other leading mathematicians of her day. The original play in German has been performed with great success at several universities in Germany and in the Theater Drachengasse in Vienna.

    A coproduction by portraittheater Vienna and Freie Universität Berlin. Scientific Board: Mechthild Koreuber, David Rowe.

    View the “Diving into Math with Emmy Noether” trailer.

  • COLLOQUIUMS: CMSA Colloquium: Strategyproof-Exposing Mechanisms Descriptions

    Speaker: Yannai Gonczarowski – Harvard

    12:00 PM-1:00 PM
    September 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

    By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

    Joint work with Ori Heffetz and Clayton Thomas.


  • CMSA EVENT: CMSA New Technologies in Mathematics: Breaking the one-mind-barrier in mathematics using formal verification

    Speaker: Johan Commelin – Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

    2:00 PM-3:00 PM
    September 14, 2022

    In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

    I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

    For more information on how to join, please see:

  • NUMBER THEORY SEMINAR: Number Theory Seminar: Symplectic Reidemeister torsion and symplectic L-functions

    Speaker: Akshay Venkatesh – IAS

    3:00 PM-4:00 PM
    September 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Many of the quantities appearing in the conjecture of Birch and Swinnerton-Dyer look suspiciously like squares. Motivated by this and related examples, we may ask if the central value of an L-function “of symplectic type” admits a preferred square root.

    The answer is no: there’s an interesting cohomological obstruction. More formally, in the everywhere unramified situation over a function field, I will describe an explicit cohomological formula for the L-function modulo squares. This is based on a purely topological result about 3-manifolds. If time permits I’ll speculate on generalizations. This is based on joint work with Amina Abdurrahman.

  • SEMINARS: Informal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)

    Speaker: Curtis McMullen – Harvard University

    4:00 PM-5:00 PM
    September 14, 2022

    This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 15th.

    Please see the seminar page for more details:

  • OPEN NEIGHBORHOOD SEMINAR: Incompleteness and infinity

    Incompleteness and infinity

    Speaker: W. Hugh Woodin – Harvard University

    4:30 PM-5:30 PM
    September 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    A natural speculation is that incompleteness is simply a by-product of infinity. Perhaps one can avoid incompleteness by simply restricting our mathematical scope to the finite. Do we lose anything in this move?

    The answer I shall argue, is both yes and no. Along the way I will discuss an entirely new approach to the Godel Incompleteness Theorems which has emerged over the last 15 years. I will also introduce some very large finite numbers which arise naturally from finite combinatorics, and indicate how by invoking these large finite numbers, any number theoretic problem of modern interest can be converted to a finitistic statement.

    It is unclear which would be more amazing for these problems of modern interest: This conversion does not always produce an equivalent problem, or that this conversion always does.

  • CMSA EVENT: CMSA Topological Quantum Matter Seminar: Geometric test for topological states of matter

    Speaker: Semyon Klevtsov – University of Strasbourg

    9:00 AM-10:00 AM
    September 21, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space.Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille)


  • CMSA EVENT: CMSA Active Matter Seminar: Limit and potential of adaptive immunity

    Speaker: Shenshen Wang – UCLA

    11:00 AM-12:00 PM
    September 21, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The adaptive immune system is able to learn from past experiences to better fit an unforeseen future. This is made possible by a diverse and dynamic repertoire of cells expressing unique antigen receptors and capable of rapid Darwinian evolution within an individual. However, naturally occurring immune responses exhibit limits in efficacy, speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical frameworks we developed to (1) explore functional impacts of non-equilibrium antigen recognition, and (2) identify conditions under which natural selection acting local in time can find adaptable solutions favorable in the long run, through exploiting environmental variations and functional constraints.

    This seminar will be held at CMSA, 20 Garden St, seminar room G-10 and on Zoom. For more information on how to join the Zoom, please see:

  • CMSA EVENT: CMSA Colloquium: Moduli spaces of graphs

    Speaker: Melody Chan – Brown

    12:30 PM-1:30 PM
    September 21, 2022
    20 Garden Street, Cambridge, MA 02138

    A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs’’ to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.


  • CMSA EVENT: CMSA New Technologies in Mathematics Seminar
    2:00 PM-3:00 PM
    September 21, 2022

    For more information, please see:

  • SEMINARS: Informal Seminar: Dynamics: From the circle to Riemann surfaces

    Speaker: Curtis McMullen – Harvard

    4:00 PM-5:00 PM
    September 21, 2022

    This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 21st.

    Please see the seminar page for more details:


  • SEMINARS: Gauge Theory and Topology Seminar: Instantons mod 2 and indefinite 4-manifolds

    Speaker: Mike Miller Eismeier – Columbia

    3:30 PM-4:30 PM
    September 23, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    This talk is on work in preparation with Ali Daemi.

    I will explain why Kim Froyshov’s mod 2 instanton invariant q_3 gives information about indefinite 4-manifolds: if H_1(W;Z/2) = 0 and W has boundary Y, then -b^+(W) <= q_3(Y) <= b^-(W). This is the first invariant known to enjoy comparable bounds for indefinite manifolds W.

    The key observation is that even when b^+(W) > 0, one can define a Donaldson invariant in the (tilde) instanton homology of boundary(W) — not in the usual instanton tilde complex, but rather a “suspension”. This suspension process accounts for the role of obstructed gluing theory, and does not destroy information about q_3 (but does destroy information about all other types of h-invariant).

    As a corollary, we show that there exist integer homology spheres with arbitrary integral surgery number S(Y_n) = n. This answers a question of Dave Auckly. Previously, the state of the art was n=2, and further progress was obstructed by the possibility that the linking matrix be indefinite.


  • CMSA EVENT: CMSA/Math Fall Gathering
    4:30 PM-6:00 PM
    September 23, 2022

    CMSA Fall Gathering will be held on September 23rd from 4:30-6:00pm. All CMSA and Math Affiliates Invited! Hot dogs, popcorn, and hot cider courtesy of Dylan and Pete’s.

  • SEMINARS: CMSA General Relativity Seminar: General-relativistic viscous fluids

    Speaker: Marcelo Disconzi – Vanderbilt University

    9:30 AM-10:30 AM
    September 29, 2022

    The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

    For information on how to join, please see: