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DTSTART;TZID=America/New_York:20221202T110000
DTEND;TZID=America/New_York:20221202T120000
DTSTAMP:20260409T152612
CREATED:20230817T164654Z
LAST-MODIFIED:20240229T111029Z
UID:10001230-1669978800-1669982400@cmsa.fas.harvard.edu
SUMMARY:Compactness and Anticompactness Principles in Set Theory
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Compactness and Anticompactness Principles in Set Theory \nAbstract: Several fundamental properties in Topology\, Algebra or Logic are expressed in terms of Compactness Principles.For instance\, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise\, we say that compactness fails. Loosely speaking\, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group\, a topological space\, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$\, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits\, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221118T110000
DTEND;TZID=America/New_York:20221118T120000
DTSTAMP:20260409T152612
CREATED:20230809T111725Z
LAST-MODIFIED:20240209T052933Z
UID:10001229-1668769200-1668772800@cmsa.fas.harvard.edu
SUMMARY:Light states in the interior of CY moduli spaces
DESCRIPTION:Member Seminar \nSpeaker: Damian van de Heisteeg \nTitle: Light states in the interior of CY moduli spaces \nAbstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction\, that is\, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points\, and find that they correspond to special points in the moduli space of the CY\, such as orbifold points and rank two attractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111822/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-11.18.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221111T110000
DTEND;TZID=America/New_York:20221111T120000
DTSTAMP:20260409T152612
CREATED:20230809T111328Z
LAST-MODIFIED:20240209T052938Z
UID:10001228-1668164400-1668168000@cmsa.fas.harvard.edu
SUMMARY:Quantum trace and length conjecture for hyperbolic knot
DESCRIPTION:Member Seminar \nSpeaker: Mauricio Romo \nTitle: Quantum trace and length conjecture for hyperbolic knot \nAbstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2\,C) Chern-Simons theory\, one can formulate a ‘length conjecture’ for the hyperbolic length of L.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221028T110000
DTEND;TZID=America/New_York:20221028T120000
DTSTAMP:20260409T152612
CREATED:20230809T110603Z
LAST-MODIFIED:20240301T080243Z
UID:10001227-1666954800-1666958400@cmsa.fas.harvard.edu
SUMMARY:Some non-concave dynamic optimization problems in finance
DESCRIPTION:Member Seminar \nSpeaker: Shuaijie Qian (Harvard CMSA) \nTitle: Some non-concave dynamic optimization problems in finance \nAbstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle\, and derives equivalent\, concave optimization problems whose value functions are still concave. In this talk\, I will present our recent work on some non-concave dynamic optimization problems\, where the concavification principle may not hold and the resulting value function is indeed non-concave. \nThe first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation\, where the average tax basis and the average mining cost serves as an approximation\, respectively. This approximation results in a non-concave value function\, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover\, the penalty method still works and converges to the value function. \nThe second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints\, which makes the concavification principle invalid\, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous\, we introduce a new definition of viscosity solution\, prove the corresponding comparison principle\, and show that a monotone\, stable\, and consistent finite difference scheme converges to the solution of the utility maximization problem. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-6/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221021T110000
DTEND;TZID=America/New_York:20221021T120000
DTSTAMP:20260409T152612
CREATED:20230809T110107Z
LAST-MODIFIED:20240301T080144Z
UID:10001226-1666350000-1666353600@cmsa.fas.harvard.edu
SUMMARY:Explicit Ramsey Graphs and Two Source Extractors
DESCRIPTION:Speaker: David Zuckerman\, Harvard CMSA/University of Texas at Austin \nTitle: Explicit Ramsey Graphs and Two Source Extractors \nAbstract: 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 high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-5/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221014T110000
DTEND;TZID=America/New_York:20221014T120000
DTSTAMP:20260409T152612
CREATED:20240214T103536Z
LAST-MODIFIED:20240301T081027Z
UID:10002676-1665745200-1665748800@cmsa.fas.harvard.edu
SUMMARY:Quantum magnet chains and Kashiwara crystals
DESCRIPTION:Speaker: Leonid Rybnikov\, Harvard CMSA/National Research University Higher School of Economics \nTitle: Quantum magnet chains and Kashiwara crystals \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101422/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.14.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221007T110000
DTEND;TZID=America/New_York:20221007T120000
DTSTAMP:20260409T152612
CREATED:20240214T105028Z
LAST-MODIFIED:20240301T081713Z
UID:10002681-1665140400-1665144000@cmsa.fas.harvard.edu
SUMMARY:Principal flow\, sub-manifold and boundary
DESCRIPTION:Member Seminar  \nSpeaker: Zhigang Yao \nTitle: Principal flow\, sub-manifold and boundary \nAbstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space\, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects\, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets\, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA\, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold\, a manifold passing through the center of the data\, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find\, use and interpret the principal sub-manifold\, by which a principal boundary can be further defined for data sets on manifolds.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220930T110000
DTEND;TZID=America/New_York:20220930T120000
DTSTAMP:20260409T152612
CREATED:20240214T105247Z
LAST-MODIFIED:20240301T081921Z
UID:10002683-1664535600-1664539200@cmsa.fas.harvard.edu
SUMMARY:Kahler geometry in twisted materials
DESCRIPTION:Member Seminar \nSpeaker: Jie Wang \nTitle: Kahler geometry in twisted materials \nAbstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong\, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction\, exact parent Hamiltonian\, conformal field theory analogous and other exact aspects. In generic flatbands\, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries\, in particular the Berry curvature and the Fubini-Study metric\, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics\, making many-body states less stable in flatbands. \nIn this talk\, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform\, but still exhibit exact properties such as model wavefunctions\, density algebra\, exact parent Hamiltonians. I will discuss both the theory of ideal flatband\, its experimental realization in Dirac materials as well as implications.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-93022/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220923T110000
DTEND;TZID=America/New_York:20220923T120000
DTSTAMP:20260409T152612
CREATED:20240214T105452Z
LAST-MODIFIED:20240301T083553Z
UID:10002685-1663930800-1663934400@cmsa.fas.harvard.edu
SUMMARY:Random determinants\, the elastic manifold\, and landscape complexity beyond invariance
DESCRIPTION:Member Seminar \nSpeaker: Ben McKenna \nTitle: Random determinants\, the elastic manifold\, and landscape complexity beyond invariance \nAbstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices\, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold\, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting\, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
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