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Events for the weeks of March 9th – 22nd

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Tue, Mar. 11 11am (MATH 350)	Number Theory Sarah Arpin X The isogeny-based cryptographic protocol CSIDH is based on the group action of the class group of a particular imaginary quadratic order on certain elliptic curves. The efficiency and security of CSIDH has inspired variant protocols, such as SCALLOP and OSIDH. Such protocols are based on the vectorization problem: Given elliptic curves E, E', find the ideal class whose action on E yields E'. In this work, we provide a general understanding of this question in the context of orientations and level structure on elliptic curves. In particular, we study a large family of generalized class groups of imaginary quadratic orders O and prove that they act freely and (essentially) transitively on the set of primitively O-oriented elliptic curves over a field k (assuming this set is non-empty) equipped with appropriate level structure. This is joint work with Wouter Castryck, Jonathan Komada Eriksen, Gioella Lorenzon, and Frederik Vercauteren. Generalized class group actions on oriented elliptic curves with level structure
Tue, Mar. 11 12:10pm (MATH …	Kempner Edmund Harriss (University of Arkansas) X Euclid's elements is regarded as an early example of proof and axiomatic methods but it also has a tradition within carpentry and construction. The straight line and circle can just as easily be regarded as abstract representations of the action of straight edge and compass just as easily as the other way round. Today we have many machines that can play the same role creating a bridge between the abstract and the physical. What potentials do they provide for realising mathematical concepts in physical space and creating manufacturing techniques? In this talk I will look at several examples of machines with mathematical models, including affine spaces, ruled and developable surfaces and the gradient present in the grain of wood. Mathematical Manufacturing since Euclid
Tue, Mar. 11 1:15pm (MATH 3…	Geometry/Analysis Tristan Léger (Yale University) X In this talk I will discuss recent and upcoming results on the boundedness of spectral projectors. The seminal work of C. Sogge gives the optimal result on any Riemannian manifold with bounded geometry for spectral windows of size 1. However when the width is smaller, the spectral projector bounds become sensitive to the global geometry of the underlying manifold. I will focus on the case of hyperbolic surfaces of infinite area, and present new estimates that hold universally in that setting. This is joint work with Jean-Philippe Anker and Pierre Germain. Spectral projector bounds on hyperbolic surfaces of infinite area Sponsored by the Meyer Fund
Wed, Mar. 12 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X In this talk, we will introduce the basic tools and terminology for future talks on Machine Learning and Statistical Applications. Fitting with the theme of this seminar, we will also touch on concepts regarding the physical meaning of "information" and its connections with Statistics. Statistics and Mathematical Physics
Wed, Mar. 12 3:30pm (MATH 2…	Algebra/Logic Joel David Hamkins (Notre Dame University) X I shall introduce and describe the subject of modal model theory, in which one studies a mathematical structure within a class of similar structures under an extension concept, giving rise to mathematically natural notions of possibility and necessity, a form of mathematical potentialism. We study the class of all graphs, or all groups, all fields, all orders, or what have you; a natural case is the class of all models of a fixed first-order theory. In this talk, I shall describe some of the resulting elementary theory, particularly the remarkable expressive power of modal graph theory. This is joint work with my Oxford student Wojciech Woloszyn. Introduction to modal model theory
Thu, Mar. 13 11:15am (MATH …	Algebraic Geometry Leo Herr X Joint work with Sara Mehidi, Marta Pieropan, Thibault Poiret Let X --> Y be a morphism of varieties and k a field. Consider the set X(k) of k-points, or solutions to the equations defining X with coordinates in k. If X = V(x^2 + y^2 - 1) for example, then the set of Q-points consists of primitive Pythagorean triples and the geometry of X shows there are infinitely many solutions. According to Hindry-Silverman, "Geometry determines Arithmetic." We want to determine the image of the map on k-points X(k) --> Y(k). Suppose X --> Y arises as the fiber over 0 of a family of varieties X' --> Y'. The geometry of the family X' --> Y' can also constrain the type of k-points that land in the image of X(k) --> Y(k), as Campana observed. Abramovich generalized this notion in a beautiful, incomplete manuscript called "birational geometry for number theorists" and gave us permission to realize this vision using log geometry. Log structures on X, Y remember enough about the families X', Y' to constrain the rational points. "Birational geometry for number theorists" for log geometers
Thu, Mar. 13 1:30pm (MATH 2…	Grad Student Seminar Édouard Heitzmann X A districting of a graph G is a partition of G into simply connected subgraphs P_i. MCMC methods are frequently used to sample the space of districtings, with Recombination Steps being a computationally inexpensive and rapidly mixing transition rule to run such a chain. This talk will define Recombination Steps, survey the literature surrounding them, and outline the proof of an irreducibility result for this proposal when G is a triangular subset of the triangular lattice. An irreducibility result for districtings of triangular subsets of the triangular lattice
Thu, Mar. 13 2:30pm (MATH 3…	Functional Analysis Jordan Watts (University of Central Michigan) X Moving from finite-dimensional calculus to an infinite-dimensional setting immediately forces one to contend with a lot of point-set topology and analysis that was less of a concern before. In this talk, we examine a classical way of taking derivates of a function between locally convex spaces from a diffeological and Sikorski perspective. We apply our results by studying several infinite-dimensional groups of relevance to symplectic topologists. Joint work with Yael Karshon. Infinite-Dimensional Calculus and Symplectic Topology
Fri, Mar. 14 11:15am (Math …	Math Edu Rebekah Jones & Courtney Hauf X In this interactive seminar, we will be discussing excerpts from Building Thinking Classrooms by Peter Liljedahl. This book focuses on research-backed strategies to foster engagement and critical thinking in the mathematics classroom. Participants will reflect on their own experiences and discuss practical ways to implement the strategies discussed in excerpts, so please look at the reading ahead of time ( link to reading). Building Thinking Classrooms Discussion
Tue, Mar. 18 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 7
Tue, Mar. 18 3:30pm (MATH 3…	Topology Alex LaJeunesse (CU Boulder) TBD
Wed, Mar. 19 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X TBA Statistical Learning
Thu, Mar. 20 11:15am (MATH …	Algebraic Geometry Ruijie Yang (Kansas) X TBD TBD Sponsored by the Meyer Fund
Thu, Mar. 20 2:30pm (MATH 3…	Functional Analysis Laura Scull (Fort Lewis College) X One common way of representing spaces with singularities is via topological groupoids. However, such a representation is not unique, and a space may be represented by many different groupoids, leading to the idea of Morita equivalence of groupoids. To work with these spaces, we define a localised bicategory of groupoids in which Morita equivalences become isomorphisms. This localisation can be done in several equivalent ways, as developed by Pronk and Roberts. Our interest lies in a particularly nice and ubiquitous class of examples, the action groupoids which represent the quotient of a space by an action of a group. Such groupoids come with their own notion of morphisms given by equivariant functors. Our aim is to connect these two viewpoints. We create a localised bicategory built on equivariant functors of groupoids, and show that for action groupoids, this is equivalent to the bicategories of Pronk and Roberts. Using this viewpoint, Morita equivalences may be defined using a certain class of equivariant projection functors, and many common conditions on the singularities can be integrated into this construction. This also gives us a way of examining invariants from equivariant homotopy to see if they can be made Morita invariant and extended to our setting. This talk is based on joint work with J. Watts and C. Farsi. The talk will include many pictures and examples illustrating the underlying geometric intuition behind the abstraction of the bicategories. Localising Action Groupoids
Thu, Mar. 20 3:35pm (MATH 3…	Probability Giorgio Cipolloni (University of Arizona) X We study the Brownian evolution of large non-Hermitian matrices and show that their log-determinant converges to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, i.e. logarithmically correlated for the parabolic distance. This gives a dynamical extension of the celebrated result by Rider and Virag (2006) proving that the fluctuations of the eigenvalues of Gaussian non-Hermitian matrices converge to a 2 dimensional log-correlated field. Our result, previously not known even in the Gaussian case, holds out of equilibrium for general matrices with i.i.d. entries. We also study the extremal values of these fields and demonstrate their logarithmic dependence on the matrix dimension. Logarithmically correlated fields from non-Hermitian random matrices

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