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2  3  4  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Holomorphic Twists and Confinement in N=1 SYM
Speaker: Justin Kulp – Perimeter Institute 9:30 AM11:00 AM October 4, 2022
Supersymmetric QFT’s are of longstanding interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and KacMoody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super YangMills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantummatterseminar/  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: Around the motivic monodromy conjecture for nondegenerate hypersurfaces
Speaker: Ming Hao Quek – Brown University 3:00 PM4:00 PM October 4, 2022 1 Oxford Street, Cambridge, MA 02138 USA
I will discuss my ongoing effort to comprehend, from a geometric viewpoint, the motivic monodromy conjecture for a “generic” complex multivariate polynomial f, namely any polynomial f that is nondegenerate with respect to its Newton polyhedron. This conjecture, due to Igusa and Denef–Loeser, states that for every pole s of the motivic zeta function associated to f, exp(2πis) is a “monodromy eigenvalue” associated to f. On the other hand, the nondegeneracy condition on f ensures that the singularity theory of f is governed, up to a certain extent, by faces of the Newton polyhedron of f. The extent to which the former is governed by the latter is one key aspect of the conjecture, and will be the main focus of my talk.
 5  CMSA EVENT: CMSA New Technologies in Mathematics: Minerva: Solving Quantitative Reasoning Problems with Language Models
Speaker: Guy GurAri – Google Research 2:00 PM3:00 PM October 5, 2022 Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformerbased language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, mathfocused dataset. Performance can be further improved using prompting and sampling techniques including chainofthought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.
For more information, please see: https://cmsa.fas.harvard.edu/techinmath/  NUMBER THEORY SEMINAR: Number Theory Seminar: Localglobal compatibility over function fields
Speaker: Daniel LiHuerta – Harvard 3:00 PM4:00 PM October 5, 2022 1 Oxford Street, Cambridge, MA 02138 USA The Langlands program predicts a relationship between automorphic representations of a reductive group G and Galois representations valued in its Lgroup. For general G over a global function field, the automorphictoGalois direction has been constructed by V. Lafforgue. More recently, for general G over a nonarchimedean local field, a similar correspondence has been constructed by Fargues–Scholze. We present a proof that the V. Lafforgue and Fargues–Scholze correspondences are compatible, generalizing localglobal compatibility from class field theory. As a consequence, the correspondences of Genestier–Lafforgue and Fargues–Scholze agree, which answers a question of Fargues–Scholze, Hansen, Harris, and Kaletha.  SEMINARS: Informal Seminar: Riemann surfaces and regular polygons
Speaker: Curtis McMullen – Harvard 4:00 PM5:00 PM October 5, 2022  CMSA EVENT: CMSA Colloquium: Quantum statistical mechanics of charged black holes and strange metals
Speaker: Professor Subir Sachedev – 4:00 PM5:00 PM October 5, 2022 1 Oxford Street, Cambridge, MA 02138 USA
The SachdevYeKitaev model was introduced as a toy model of interacting fermions without any particlelike excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.
 6  OTHER MATHEMATICS DEPARTMENT EVENTS: Mathematics for Human Flourishing: Francis Su
Speaker: Francis Su – Harvey Mudd College 4:30 PM6:00 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.
 7  CMSA EVENT: CMSA Algebraic Geometry in String Theory: Scattering Diagrams from Holomorphic Discs in Log Calabi–Yau Surfaces
Speaker: Sam BardwellEvans – Boston University 9:30 AM10:30 AM October 7, 2022 20 Garden Street, Cambridge, MA 02138
In this talk, we construct special Lagrangian fibrations for log Calabi–Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebrogeometric scattering diagrams of Gross–Pandharipande–Siebert and Gross–Hacking–Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov–Witten invariants to log GromovWitten invariants. This talk is based on joint work with ManWai Mandy Cheung, Hansol Hong, and YuShen Lin.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraicgeometryinstringtheory/  SEMINARS: Gauge Theory and Topology Seminar: Exotic 4manifolds with signature zero
Speaker: Inanc Baykur – University of Massachusetts Amherst / Harvard 3:30 PM4:30 PM October 7, 2022 1 Oxford Street, Cambridge, MA 02138 USA
We will talk about our recent construction of the smallest closed exotic 4manifolds with signature zero known to date. Our novel examples are derived from fairly special small Lefschetz fibrations we build, with spin and nonspin monodromies. This is joint work with N. Hamada.
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9  10  11  12  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Engineering topological phases with a superlattice potential
Speaker: Jennifer Cano – Stony Brook University and Flatiron Institute 9:00 AM10:00 AM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA
We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spinorbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long soughtafter goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernalstacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
 CMSA EVENT: CMSA Colloquium: Complete disorder is impossible: some topics in Ramsey theory
Speaker: James Cummings – Carnegie Mellon University 12:30 PM1:30 PM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA
The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasising the diverse ideas which are at play in this area.
 NUMBER THEORY SEMINAR: Number Theory Seminar: Integrality properties of the Betti moduli space
Speaker: Hélène Esnault – FU Berlin 3:00 PM4:00 PM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA We study them, in particular showing on a smooth complex quasiprojective variety the existence of $ℓ$adic absolutely irreducible local systems for all $ℓ$ the moment there is a complex irreducible topological local system. The proof is purely arithmetic. This is work in progress with Johan de Jong, relying in part on earlier work with Michael Groechenig.  SEMINARS: Informal Seminar: Billiards and Teichmüller theory
Speaker: Curtis McMullen – Harvard 4:00 PM5:00 PM October 12, 2022  OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: On the capset problem and the slice rank polynomial method
Speaker: Lisa Sauermann – MIT 4:30 PM5:30 PM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA In 2016, Ellenberg and Gijswijt made a breakthrough on the famous capset problem, which asks about the maximum size of a subset of (F_3)^n not containing a threeterm arithmetic progression. They proved that any such set has size at most 2.756^n. Their proof was later reformulated by Tao, introducing what is now called the slice rank polynomial method. This talk will explain Tao’s proof of the EllenbergGijswijt bound for the capset problem, and discuss some related problems.
 13  SEMINARS: Algebraic Dynamics Seminar: Integralaffine structures and degenerations of K3 surfaces
Speaker: Philip Engel – University of Georgia 4:00 PM6:00 PM October 13, 2022 I will discuss joint work with V. Alexeev which builds a correspondence between degenerations of polarized K3 surfaces and integralaffine structures on the 2sphere containing a weighted balanced graph. Under this correspondence, natural questions emerge about the dynamics of the straight line flow on integralaffine manifolds. In particular, we will explore (1) the relationship between closed trajectories and immersed elliptic curves in the K3 surface, and (2) the possibility of a tropical YauZaslow formula for counting immersed trees. For more information, please see: https://people.math.harvard.edu/~demarco/AlgebraicDynamics/
 14  CMSA EVENT: CMSA Algebraic Geometry in String Theory: Singularities of the quantum connection on a Fano variety
Speaker: Daniel Pomerleano – UMass Boston 9:30 AM10:30 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 farreaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semisimple 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/algebraicgeometryinstringtheory/  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 AM12:00 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 DeligneMumford moduli space of stable rational curves, which is unramified over the real locus of the DeligneMumford 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 finitedimensional 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 PM4:30 PM October 14, 2022 1 Oxford Street, Cambridge, MA 02138 USA
Representations of 3manifold 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 CassonLin invariant, and the A polynomial. In 2010, KronheimerMrowka showed that the fundamental group of every nontrivial 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 KronheimerMrowka’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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16  17  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Topological Wick Rotation and Holographic duality
Speaker: Liang Kong – Sustech 9:00 AM10:30 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 finitegroup 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/quantummatterinmathematicsandphysics/  OTHER MATHEMATICS DEPARTMENT EVENTS: Jameel AlAidroos Mathematical Pedagogy Lecture Series
3:00 PM6:00 PM October 17, 2022 1 Oxford Street, Cambridge, MA 02138 USA Jameel AlAidroos 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 questionasking 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 voiceover 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 AlAidroos Mathematical Pedagogy Lecture Series When: October 17, 2022 Where: Hall E, Science Center, 1 Oxford Street, Cambridge, MA, 02138 Register for the InPerson 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
 18  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: On the sixdimensional origin of noninvertible symmetries
Speaker: Michele Del Zotto – Uppsala University) 9:00 AM10:30 AM October 18, 2022
I will present a review about recent progress in chartin noninvertible symmetries for fourdimensional quantum field theorie that have a sixdimensional origin. These include in particular N= supersymmetric YangMills theories, and also a large class of N= supersymmetric theories which are conformal and do not have conventional Lagrangian description (the socalled theories of “clas S”). Among the main results, I will explain criteria for identifyin examples of systems with intrinsic and nonintrinsic noninvertibl symmetries, as well as explore their higher dimensional origin. Thi seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan and Justin Kaidi.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantummatterseminar/  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: HarvardMIT Algebraic Geometry Seminar: Old and new geometry for orbital integrals
Speaker: Oscar Kivinen – EPFL 3:00 PM4:00 PM October 18, 2022
I will explain how to reinterpret invariant distributions on padic GL_n and its Lie algebra using symmetric functions. This reinterpretation, combined with some old results of Waldspurger, allows us to compute the Shalika germs of tamely ramified regular semisimple elements in GL_n and for example pointcounts of compactified Jacobians on plane curve singularities. I will exposit the method and some interesting consequences such as how to tdeform many of the results using Ktheory of Hilbert schemes of points on C^2. Time permitting, I will discuss the relation to triply graded knot homology. Based on joint work with ChengChiang Tsai.
Webpage: https://sites.google.com/view/harvardmitag
 19  CMSA EVENT: CMSA Colloquium: The Mobility Edge of Lévy Matrices
Speaker: Patrick Lopatto – Brown University 12:45 PM1:45 PM October 19, 2022 20 Garden Street, Cambridge, MA 02138
Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alphastable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavytailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.
 CMSA EVENT: CMSA New Technologies in Mathematics: Towards Faithful Reasoning Using Language Models
Speaker: Antonia Creswell – DeepMind 2:00 PM3:00 PM October 19, 2022
Language models are showing impressive performance on many natural language tasks, including questionanswering. However, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this, we will introduce SelectionInference, a faithful reasoning model, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy.
For more information, please see: https://cmsa.fas.harvard.edu/event_category/newtechnologiesinmathematicsseminarseries/  NUMBER THEORY SEMINAR: Number Theory Seminar: Arithmetic statistics via graded Lie algebras
Speaker: Jef Laga – Princeton 3:00 PM4:00 PM October 19, 2022 1 Oxford Street, Cambridge, MA 02138 USA I will explain how various results in arithmetic statistics by Bhargava, Gross, Shankar and others on 2Selmer groups of Jacobians of (hyper)elliptic curves can be organised and reproved using the theory of graded Lie algebras, following earlier work of Thorne. This gives a uniform proof of these results and yields new theorems for certain families of nonhyperelliptic curves. I will also mention some applications to rational points on certain families of curves.  SEMINARS: Informal Seminar: Arithmetic chaos in the regular 12gon: open problems
Speaker: Curtis McMullen – Harvard 4:00 PM5:00 PM October 19, 2022  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Symmetric Mass Generation
Speaker: Professor Yizhuang You – UC San Diego 4:00 PM5:30 PM October 19, 2022 20 Garden Street, Cambridge, MA 02138
Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strongcoupling nonperturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
 20  CMSA EVENT: CMSA Active Matter: Attempts at understanding human axial elongation and patterning
Speaker: Sharad Ramanathan – Harvard 12:00 PM1:00 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/activematterseminar6/
 21  CMSA EVENT: CMSA Algebraic Geometry in String Theory: The index of Mtheory
Speaker: Nicolo Piazzalunga – Rutgers University 9:30 AM10:30 AM October 21, 2022 20 Garden Street, Cambridge, MA 02138
I’ll introduce the higherrank Donaldson–Thomas theory for toric Calabi–Yau threefolds, within the setting of equivariant Ktheory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genuszero Gromov–Witten theory of noncompact toric varieties.  CMSA EVENT: CMSA Member Seminar: Explicit Ramsey Graphs and Two Source Extractors
Speaker: David Zuckerman – Harvard CMSA/The University of Texas at Austin 11:00 AM12:00 PM October 21, 2022 1 Oxford Street, Cambridge, MA 02138 USA
Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2. Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs. This turns out to relate to the question of extracting highquality randomness from two independent lowquality sources. I’ll explain this connection and our recent exponential improvement in constructing twosource extractors.
This seminar will begin at 11:00am and lunch will follow at 12:00pm.  SEMINARS: Mathematical Logic Seminar
Speaker: Assaf Shani – Harvard University 2:00 PM3:00 PM October 21, 2022
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23  24  25  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Unorientable Quantum Field Theories: from crosscaps to holography
Speaker: João Caetano – CERN 9:00 AM10:30 AM October 25, 2022
In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state. In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4manifold. I will show how to do this in the example of N=4 Supersymmetric YangMills, discuss its holographic description and present a new solvable setup of AdS/CFT. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantummatterseminar/
 HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: Harvard/MIT Algebraic Geometry Seminar: Cohomology of moduli spaces of curves
Speaker: Samuel Payne – 3:00 PM4:00 PM October 25, 2022 1 Oxford Street, Cambridge, MA 02138 USA
Cohomology groups of moduli spaces of curves are fruitfully studied from several mathematical perspectives, including geometric group theory, stably homotopy theory, and quantum algebra. Algebraic geometry endows these cohomology groups with additional structures (Hodge structures and Galois representations), and the Langlands program makes striking predictions about which such structures can appear. In this talk, I will present recent results inspired by, and in some cases surpassing, such predictions. These include the vanishing of odd cohomology on moduli spaces of stable curves in degrees less than 11, generators and relations for H^11, and new constructions of unstable cohomology on M_g. Based on joint work with Jonas Bergström and Carel Faber; with Sam Canning and Hannah Larson; with Melody Chan and Søren Galatius; and with Thomas Willwacher.
 26  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
Speaker: Bruno Mera – Tohoku University 9:00 AM10:00 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 momentumspace 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 translationinvariant (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 wellknown 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 PM1:30 PM October 26, 2022 1 Oxford Street, Cambridge, MA 02138 USA
A kclique 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 kcliques in a given graph?”. Even just detecting whether an nvertex graph contains a kClique has long been known to be NPcomplete 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 bruteforce algorithm runs in polynomial time, O(n^k), and can list all kcliques in the graph; though O(n^k) time is far from practical. As the number of kcliques in an nvertex graph can be Omega(n^k), the bruteforce algorithm is in some sense optimal, but only if there are Omega(n^k) kcliques. In this talk we will show how to list kcliques faster when the input graph has few kcliques, with running times depending on the number of vertices n, the number of edges m, the number of kcliques 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 PM3:00 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/newtechnologiesinmathematicsseminarseries/
 NUMBER THEORY SEMINAR: Number theory seminar: Non additive geometry and Frobenius correspondences
Speaker: Shai Haran – Technion 3:00 PM4:00 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 bioperads, 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 PM5:00 PM October 26, 2022  OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood: From Diophantus to Bitcoin: why are elliptic curves everywhere?
Speaker: Alvaro LozanoRobledo – University of Connecticut 4:30 PM5:30 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.
 27  SEMINARS: Algebraic Dynamics: Polynomials, branched covers, and trees
Speaker: Becca Winarski – College of the Holy Cross 4:00 PM6:00 PM October 27, 2022 Thurston proved that a postcritically finite branched cover of the plane is either equivalent to a polynomial (that is: conjugate via a mapping class) or it has a topological obstruction. We use topological techniques – adapting tools used to study mapping class groups – to produce an algorithm that determines when a branched cover is equivalent to a polynomial, and if it is, determines which polynomial a topological branched cover is equivalent to. This is joint work with Jim Belk, Justin Lanier, and Dan Margalit.
For more information, please see: https://people.math.harvard.edu/~demarco/AlgebraicDynamics/
 28  CMSA EVENT: CMSA Algebraic Geometry in String Theory: 2Categories and the Massive 3d AModel
Speaker: Ahsan Khan – IAS 9:30 AM10:30 AM October 28, 2022 20 Garden Street, Cambridge, MA 02138
I will outline the construction of a 2category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two and three dimensions, combined with a threedimensional version of the Gaiotto–Moore–Witten web formalism.
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/algebraicgeometryinstringtheory/  HARVARDMIT COMBINATORICS SEMINAR: The tropical fundamental group
Speaker: Eric Katz – OSU 3:00 PM4:00 PM October 28, 2022 1 Oxford Street, Cambridge, MA 02138 We discuss recent joint work with Kyle Binder on defining the unipotent fundamental group of tropical varieties. This fundamental group arises from the Tannakian formalism using tropical vector bundles with integrable connection. By employing the Orlik–Solomon theorem, we prove that this computes the unipotent completion of the fundamental group of algebraic varieties with smooth tropicalization. ======================================================= http://math.mit.edu/seminars/combin/ =============================================
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