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  • OTHER MATHEMATICS DEPARTMENT EVENTS: Mathematics for Human Flourishing: Francis Su

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Mathematics for Human Flourishing: Francis Su

    Speaker: Francis Su – Harvey Mudd College

    4:30 PM-6:00 PM
    October 6, 2022

    Math is more than just a way to describe the world, and it is more than just a set of skills, like doing arithmetic and factoring a quadratic. Math is a deeply human enterprise that fulfills basic human longings, such as for beauty and truth. When properly engaged, it builds virtues like persistence, creativity, and a competence to solve new problems. These virtues will serve you well no matter what you do in life. It was an incarcerated man–now his friend–that helped distinguished mathematician Francis Su see this more clearly than ever before.

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  • CMSA EVENT: CMSA Algebraic Geometry in String Theory: Singularities of the quantum connection on a Fano variety

    Speaker: Daniel Pomerleano – UMass Boston

    9:30 AM-10:30 AM
    October 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty. 
     
     I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau–Ginzburg model intrinsically attached to (M,D).  

    This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraic-geometry-in-string-theory/

  • CMSA EVENT: CMSA Member Seminar: Quantum magnet chains and Kashiwara crystals

    Speaker: Leonid Rybnikov – Harvard CMSA/National Research University Higher School of Economics

    11:00 AM-12:00 PM
    October 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.


     

  • SEMINARS: Gauge Theory and Topology: The existence of irreducible SU(2) representations of link groups

    Speaker: Boyu Zhang – University of Maryland

    3:30 PM-4:30 PM
    October 14, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Representations of 3-manifold groups into groups such as SU(2) and SL(2,C) have been actively studied for decades.  Many topological invariants are defined by considering these representations, such as the Casson invariant, the Casson-Lin invariant, and the A polynomial.  In 2010, Kronheimer-Mrowka showed that the fundamental group of every non-trivial knot in S^3 admits an irreducible representation in SU(2) such that the image of the meridian is traceless, which answered a conjecture of Cooper.  In this talk, I will present a result that generalizes Kronheimer-Mrowka’s theorem to the case of links.  We show that for every link L that is not the unknot, the Hopf link, or a connected sum of Hops links, its fundamental group admits an irreducible SU(2) representation such that the image of every meridian is traceless.  The proof is based on an excision formula of singular instanton Floer homology.  This is joint work with Yi Xie.


     

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  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Topological Wick Rotation and Holographic duality

    Speaker: Liang Kong – Sustech

    9:00 AM-10:30 AM
    October 17, 2022

    I will explain a new type of holographic dualities between n+1D topological orders with a chosen boundary condition and nD (potentially gapless) quantum liquids. It is based on the idea of topological Wick rotation, a notion which was first used in arXiv:1705.01087 and was named, emphasized and generalized later in arXiv:1905.04924. Examples of these holographic dualities include the duality between 2+1D toric code model and 1+1D Ising chain and its finite-group generalizations (independently discovered by many others); those between 2+1D topological orders and 1+1D rational conformal field theories; and those between n+1D finite gauge theories with a gapped boundary and nD gapped quantum liquids. I will also briefly discuss some generalizations of this holographic duality and its relation to AdS/CFT duality.


    For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/quantum-matter-in-mathematics-and-physics/

  • OTHER MATHEMATICS DEPARTMENT EVENTS: Jameel Al-Aidroos Mathematical Pedagogy Lecture Series

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Jameel Al-Aidroos Mathematical Pedagogy Lecture Series

    3:00 PM-6:00 PM
    October 17, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Jameel Al-Aidroos was a treasured colleague and a master of a myriad of things. He could simplify a mathematical idea and present a question or comment in a way that could bring his students to view concepts from new perspectives. Likewise, when he worked with graduate students around pedagogy and with school teachers around the joys of engaging with mathematics, the thoughtful way he approached teaching and mentorship made a big difference. Watching Jameel teach motivated and inspired both novice and veteran teachers to become better instructors and to bring their best selves forward. His superpower as a teacher was asking just the right questions to focus students’ attention on the core of the mathematical idea.

    Through a number of seminars and workshops, Jameel shared his question-asking approach and pedagogical skills with graduate students and faculty. An astute and careful listener, a masterful communicator, and a deep thinker, he forged impactful connections. As a mentor and colleague, Jameel was without equal: he applied himself wholeheartedly to hone his craft in the classroom and as a mentor. He was quick to volunteer to do whatever was needed to promote team projects and through this, we discovered his enormous talents as an interviewer, film editor, and voice-over artist, among other things. It seemed there were no tasks he did not choose to rise to and polish, while consistently taking a step out of the limelight to let his students and colleagues shine.

    The grace and generosity of spirit he extended to his students and colleagues are an indelible part of his legacy. Jameel carried this grace and generosity throughout his long battle with cancer. We honor his contributions and dedication to teaching and learning at Harvard via this speaker series as a small way to remember Jameel’s extraordinary warmth of character and pedagogical skills. He motivated and inspired his students and colleagues; through this series, we hope to celebrate and keep alive that legacy by bringing speakers who share new perspectives on mathematics and pedagogy, and motivate us to reflect on our professional roles.

    Jameel Al-Aidroos Mathematical Pedagogy Lecture Series

    When: October 17, 2022

    Where: Hall E, Science Center, 1 Oxford Street, Cambridge, MA, 02138

    Register for the In-Person Event.

    Register for the Online Event.

    Download a detailed PDF schedule of lectures and events.

    Schedule
    3 p.m. – 3:50 p.m.

    Aubrey Clayton | Author of Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science

    Thinking Slowly about Probability and Statistics

    3:50 p.m. – 4 p.m.

    Break

    4 p.m. – 4:50 p.m.

    Juliana Belding | Associate Professor of the Practice of Mathematics at Boston College

    Working with Secondary Math Teachers: What Mathematicians can Offer and Learn

    5 p.m. – 6 p.m.

    Refreshments in The Austine & Chilton McDonnell Common Room, Science Center 4th floor.

     

    Organizers

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  • CMSA EVENT: CMSA Active Matter: Attempts at understanding human axial elongation and patterning

    Speaker: Sharad Ramanathan – Harvard

    12:00 PM-1:00 PM
    October 20, 2022
    20 Garden Street, Cambridge, MA 02138

    Some of the most dramatic events during human development is the axial elongation of the embryo with concomitant changes in the geometry and composition of the underlying tissues. The posterior part of the embryo gives rise to the spinal cord, vertebral column, ribcage, back muscles, and dermis.  In this talk, I will present our attempts at coaxing human embryonic stem cells to form these structures of the early human embryo that closely recapitulate the geometry, relative arrangements, composition, and dynamics of development of the early spinal cord flanked progenitors of the musculoskeletal system. Our goal was to do so, such that we could build hundreds of these organoids at a time. I will also present preliminary results for the use of this system to understand key events during early human development through imaging and genetic perturbations.


    This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/active-matter-seminar-6/

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  • CMSA EVENT: CMSA Topological Quantum Matter Seminar: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry

    Speaker: Bruno Mera – Tohoku University

    9:00 AM-10:00 AM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constrains, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a  Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.


     

  • CMSA EVENT: CMSA Colloquium: Clique listing algorithms

    Speaker: Virginia Vassilevska Williams – MIT

    12:30 PM-1:30 PM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history.
    A fundamental question, with many applications, is “How fast can one list all k-cliques in a given graph?”.
    Even just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant, such as 3 or 4 (independent of n), even the brute-force algorithm runs in polynomial time, O(n^k), and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k), the brute-force algorithm is in some sense optimal, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques, with running times depending on the number of vertices n, the number of edges m, the number of k-cliques T and more. We will focus on the case when k=3, but we will note some extensions.
    (Based on joint work with Andreas Bjorklund, Rasmus Pagh, Uri Zwick, Mina Dalirrooyfard, Surya Mathialagan and Yinzhan Xu)

  • CMSA EVENT: CMSA New Technologies Seminar: From Engine to Auto
    2:00 PM-3:00 PM
    October 26, 2022

    Speakers: João Araújo (Mathematics Department, Universidade Nova de Lisboa)
    and Michael Kinyon (Department of Mathematics, University of Denver)

    Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type, etc.
    In this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups, loops, semigroups, logic algebras, lattices and generalizations, quandles, and many more.

     

    For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/new-technologies-in-mathematics-seminar-series/


  • NUMBER THEORY SEMINAR: Number theory seminar: Non additive geometry and Frobenius correspondences

    Speaker: Shai Haran – Technion

    3:00 PM-4:00 PM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    The usual language of algebraic geometry is not appropriate for arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace s rings by the collection of “vectors” or by bi-operads, and another based on “matrices” or props. Once one understands the delicate commutativity condition one can proceed following Grothendieck’s footsteps exactly. The props, when viewed up to conjugation, give us new commutative rings with Frobenius endomorphisms.


     

  • SEMINARS: Informal Seminar: Unramified correspondences

    Speaker: Aaron Landesman – Harvard

    4:00 PM-5:00 PM
    October 26, 2022

    This seminar will be held in Science Center 530 at 4:00pm on Wednesday, October 26th.

    Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem

     

  • OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood: From Diophantus to Bitcoin: why are elliptic curves everywhere?

    Speaker: Alvaro Lozano-Robledo – University of Connecticut

    4:30 PM-5:30 PM
    October 26, 2022
    1 Oxford Street, Cambridge, MA 02138 USA

    Elliptic curves are ubiquitous in number theory, algebraic geometry, complex analysis, cryptography, physics, and beyond. They were present in Diophantus’ Arithmetica (3rd century AD) and, nowadays, they are more relevant than ever as a key ingredient in the algorithms that, for instance, secure Bitcoin transactions or encrypt WhatsApp messages. In this talk, we will introduce elliptic curves, explain their central role in mathematics, and discuss related open problems and applications.


     

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