BEGIN:VCALENDAR VERSION:2.0 METHOD:PUBLISH PRODID:-//Mathematics Department//NONSGML mathical.php//EN X-WR-CALNAME:Mathematics Department BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c6f7@math.dartmouth.edu DTSTART;TZID=America/New_York:20260210T143000 DTEND;TZID=America/New_York:20260210T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Lea Beneish: Towards Artin’s conjecture on $p$-adic forms in low degree DESCRIPTION:Let $F$ be a homogeneous polynomial of degree $n$ in at least $d^2 +1$ variables over the p-adic numbers\, $\\mathbb{Q}_p$ . Artin conjectured that such $F$ always have nontrivial zeros in any $p$-adic field. Although this has been shown to be false in general\, the conjecture is still widely believed to be true for prime degree forms. This conjecture holds for d=2 and d=3 due to Hasse and Lewis\, respectively. By the work of Ax and Kochen\, the conjecture is also known to hold whenever the characteristic of the residue field is sufficiently large. In this talk\, we will explore recent progress for low degree forms towards making bounds on the size of the residue field effective. A wide range of techniques are needed\, including Bertini theorems\, point counting on curves over finite fields\, and computation. This is joint work with Christopher Keyes. LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c772@math.dartmouth.edu DTSTART;TZID=America/New_York:20260212T130000 DTEND;TZID=America/New_York:20260212T140000 CATEGORIES:Topology Seminar SUMMARY:Porter Morgan: TBA LOCATION:Kemeny 307 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c7a7@math.dartmouth.edu DTSTART;TZID=America/New_York:20260212T131500 DTEND;TZID=America/New_York:20260212T141500 CATEGORIES:Combinatorics Seminar SUMMARY:Sergi Elizalde: Cylindric growth diagrams\, walks in simplices\, and exclusion processes DESCRIPTION:We establish bijections between three classes of combinatorial objects that have been studied in different contexts: lattice walks in simplicial regions as introduced by Mortimer--Prellberg\, standard cylindric tableaux as introduced by Gessel--Krattenthaler and Postnikov\, and sequences of states in the totally asymmetric simple exclusion process on a cycle. This perspective allows us to translate symmetries from one setting into another\, revealing unexpected properties of these objects.\n\nSpecifically\, we show that a recent bijection of Courtiel et al. between certain simplicial walks with forward and backward steps is equivalent to a cylindric analogue of the Robinson--Schensted correspondence.\nOriginally defined by Neyman by iterating an insertion operation\, we provide an alternative description of this correspondence by introducing a cylindric version of Fomin's growth diagrams.\nThis natural description elucidates the symmetry of the correspondence\, and it allows us to interpret the above walks as oscillating cylindric tableaux. LOCATION:Kemeny 307 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c7fd@math.dartmouth.edu DTSTART;TZID=America/New_York:20260212T151500 CATEGORIES:Math Colloquium SUMMARY:Bridget Tenner: Majority relations: how do ranked ballots shake out? DESCRIPTION:Suppose you have an election in which each voter ranks the full slate of candidates. If we want to draw an aggregated conclusion from all of the ballots cast\, what is the "winning" candidate ranking? We will study this question on so-called Condorcet domains of tiling type\, which can be defined in terms of rhombic tilings of certain polygons (equivalently\, in terms of reduced decompositions of permutations). We can then use heaps and poset theory to show important properties of the majority relation in these domains. We will demonstrate these results by computing the majority relation explicitly for several important classes.\n\nThis talk is based on joint work with Vic Reiner.\n LOCATION:Kemeny 007 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c873@math.dartmouth.edu DTSTART;TZID=America/New_York:20260217T143000 DTEND;TZID=America/New_York:20260217T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Louis Gaudet: Counting biquadratic number fields that admit quaternionic or dihedral extensions DESCRIPTION:Many interesting problems in arithmetic statistics involve counting number fields (ordered by their discriminants\, say) with certain properties. In joint work with Siman Wong (UMass Amherst)\, we establish asymptotic formulae for the number of biquadratic extensions of $\\mathbb{Q}$ that admit a degree-2 extension with Galois group $G$\, where $G$ is either the quaternion group or the dihedral group (of order 8). We will discuss these results and how they are proved\, and we will discuss their significance with regard to a theorem of Tate on lifts of projective Galois representations.  LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c8b8@math.dartmouth.edu DTSTART;TZID=America/New_York:20260217T153000 CATEGORIES:Functional Analysis Seminar SUMMARY:Mohammad Javad Latifi : Nonlinear Fourier Analysis for Loop Groups DESCRIPTION:This is an introductory talk on loop groups: the group of maps from the unit circle into a Lie group G\, with pointwise multiplication. Classical Fourier analysis organizes spectral information through linear sums of modes. Nonlinear Fourier analysis replaces this sum with an ordered product of simple G-valued factors\, producing a group-valued loop as the spectral data. I will explain how the same product structure appears as transfer matrices in one-dimensional lattice models and how it encodes their partition functions. The talk will end with scattering for a discrete Dirac operator as a concrete example of this nonlinear Fourier transform. LOCATION:Kemeny 343 URL:https://math.dartmouth.edu/~funct-an/ END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c8fe@math.dartmouth.edu DTSTART;TZID=America/New_York:20260219T131500 DTEND;TZID=America/New_York:20260219T141500 CATEGORIES:Combinatorics Seminar SUMMARY:Michelle Wachs: Tree Specht modules and Filippov algebras DESCRIPTION:Specht modules play a fundamental role in the representation theory of the symmetric group\, providing a complete set of irreducible representations. Each Specht module can be described by a presentation in which the generators are Young tableaux of a fixed shape\, and the relations are column and Garnir relations. In recent work with Friedmann and Hanlon\, we introduce generalizations of these concepts using trees\, which we then apply to the study of the free Filippov algebra. In this talk\, I will first review the theory of Specht modules and then discuss our generalizations and their applications. LOCATION:Kemeny 307 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c940@math.dartmouth.edu DTSTART;TZID=America/New_York:20260219T151500 CATEGORIES:Math Colloquium SUMMARY:Michelle Wachs: Chromatic symmetric functions and related structures DESCRIPTION:The chromatic symmetric function of a graph is a symmetric function analog of the classical chromatic polynomial. These symmetric functions were introduced by Stanley in 1995 in connection with his work with Stembridge on immanants. A topic of active research in algebraic combinatorics is based on the simple question of determining which graphs have an e-positive chromatic symmetric function. The Stanley-Stembridge Conjecture\, which was proved just last year by Hikita\, provides a class of such graphs. \n\nAs a means of addressing the Stanley-Stembridge Conjecture\, connections to other structures\, such as the cohomology of Hessenberg varieties and representations of Hecke algebras\, have been developed. These connections involve a refinement of the chromatic symmetric functions\, introduced by Shareshian and myself. In this talk\, after presenting basic background\, I will discuss these connections\, recent developments\, and still open questions. LOCATION:Kemeny 007 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c99d@math.dartmouth.edu DTSTART;TZID=America/New_York:20260224T143000 DTEND;TZID=America/New_York:20260224T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Michael Cerchia: CANCELED LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351c9cd@math.dartmouth.edu DTSTART;TZID=America/New_York:20260226T131500 DTEND;TZID=America/New_York:20260226T141500 CATEGORIES:Combinatorics Seminar SUMMARY:Pete Winkler: Paint Blending DESCRIPTION:A high school student named Tejo Madhavarapu sent me a puzzle he composed. I'll explain how we turned it into a (somewhat surprising\, to me) theorem. LOCATION:Kemeny 307 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351ca05@math.dartmouth.edu DTSTART;TZID=America/New_York:20260226T151500 CATEGORIES:Math Colloquium SUMMARY:Dongbin Xiu: Data Driven Modeling for Scientific Discovery and Digital Twins DESCRIPTION:We present a data-driven modeling framework for scientific discovery\, termed Flow Map Learning (FML). This framework enables the construction of accurate predictive models for complex systems that are not amenable to traditional modeling approaches. By leveraging data and the expressiveness of deep neural networks (DNNs)\, FML facilitates long-term system modeling and prediction even when governing equations are unavailable.\n\nFML is particularly powerful in the context of Digital Twins\, an emerging concept in digital transformation. With sufficient offline learning\, FML enables the construction of simulation models for key quantities of interest (QoIs) in complex Digital Twins\, when direct mathematical modeling of the QoIs is infeasible. During the online execution of a Digital Twin\, the learned FML model can simulate the QoIs without reverting to the computationally intensive Digital Twin simulation model. As a result\, FML serves as an enabling methodology for real-time control and optimization for complex systems. LOCATION:Kemeny 007 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351ca51@math.dartmouth.edu DTSTART;TZID=America/New_York:20260303T142500 DTEND;TZID=America/New_York:20260303T152500 CATEGORIES:Applied and Computational Mathematics Seminar SUMMARY:Daniel Sheldon '99: The state of the art in differentially private synthetic data DESCRIPTION:Differential privacy has emerged as a leading standard for privacy protection\, with significant adoption by both commercial and governmental enterprises. Many common computations on data can be made differentially private\, but one of the most appealing uses of differential privacy is the generation of synthetic data. Synthetic data is intended to be broadly representative of the source data\, with the goal of allowing downstream users to accurately perform a wide range of computations without further restrictions on data access.\n\nIn this talk I will review both the promise and the inherent limitations of private synthetic data. I will introduce the select–measure–reconstruct paradigm\, which recent benchmarks show to outperform other approaches for generating differentially private synthetic data\, and explain the core ideas that make it effective. A central challenge is how to combine noisy\, differentially private measurements into a coherent global model of the data distribution. I will describe Private-PGM\, a key technical approach for the reconstruction phase\, in which noisy statistics are reconciled into a consistent representation from which synthetic records can be sampled. Finally\, I will describe AIM\, a state-of-the-art generator\, and conclude with recent advances and open questions. LOCATION:Kemeny 307 and Zoom URL:https://dartmouth.zoom.us/j/97782769511?pwd=r10W9MUq6snfUlmFbzQrcuZts5txq0.1 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351caaa@math.dartmouth.edu DTSTART;TZID=America/New_York:20260303T143000 DTEND;TZID=America/New_York:20260303T133000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Dori Bejleri : The root stack valuative criterion for good moduli spaces DESCRIPTION:Given an Artin stack with a good moduli space\, the morphism to the good moduli space behaves in many ways like a proper map despite rarely being separated. In this talk\, I will discuss a strong version of the existence part of the valuative criterion of properness for good moduli space morphisms which generalizes a recent result of Bresciani-Vistoli for tame stacks. This valuative criterion does not require an extension of DVRs and thus is more suitable for arithmetic applications. I will also describe several such applications including to homogeneous spaces for reductive groups\, rational points on stacks\, and the geometry of Fano fibrations over curves. LOCATION:Kemeny 343 URL:https://math.dartmouth.edu/~zahlen/ END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351caf0@math.dartmouth.edu DTSTART;TZID=America/New_York:20260303T153000 DTEND;TZID=America/New_York:20260303T163000 CATEGORIES:Functional Analysis Seminar SUMMARY:Junhao Shen: Reducible Operator in Factors DESCRIPTION:Let H be a separable complex Hilbert space\, and let B(H) denote the set of bounded linear operators on H. The concept of reducible operators was introduced by P. Halmos in 1968: an operator T in B(H) is reducible if it has nontrivial reducing closed subspaces in H. In his famous list of “Ten Problems in Hilbert Space\,” he asked whether every bounded linear operator on H is a norm limit of reducible operators. It is not hard to see that on a finite-dimensional Hilbert space\, the answer is negative. In the infinite-dimensional space case\, this question was answered affirmatively by D. Voiculescu using his celebrated non‑commutative Weyl–von Neumann theorem.\n\nA von Neumann algebra is a self-adjoint subalgebra of B(H) that is closed in the weak operator topology and contains the identity of B(H). A factor is a von Neumann algebra whose center consists only of scalar multiples of the identity. Factors were further classified by Murray and von Neumann into type I\, II\, and III factors. By definition\, B(H) is a type I factor.\n\nIn this talk\, we will discuss the concept of reducible operators in factors and study the norm‑density properties of reducible operators in various types of factors by extending Voiculescu’s non‑commutative Weyl–von Neumann theorem to the setting of von Neumann algebras. More specifically\, we will show that the set of reducible operators is norm dense in properly infinite factors\, while this need not be the case in finite factors. LOCATION:Kemeny 343 URL:https://math.dartmouth.edu/~funct-an/ END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cb45@math.dartmouth.edu DTSTART;TZID=America/New_York:20260305T131500 DTEND;TZID=America/New_York:20260305T141500 CATEGORIES:Combinatorics Seminar SUMMARY:Colin Defant: Braid Group Presentations and Triangulations of the Permutahedron DESCRIPTION:For each finite Coxeter group W and each standard Coxeter element of W\, we construct a regular triangulation of the W-permutahedron. Our proof relies on the theory of total linear stability for Dynkin quivers. We also explore several notable combinatorial properties of these triangulations that relate the Bruhat order\, the noncrossing partition lattice\, and Cambrian congruences. Each triangulation gives an explicit mechanism for relating two different presentations of the corresponding braid group (the standard Artin presentation and Bessis's dual presentation). This is joint work with Melissa Sherman-Bennett and Nathan Williams. \n LOCATION:Kemeny 307 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cb8c@math.dartmouth.edu DTSTART;TZID=America/New_York:20260310T153000 DTEND;TZID=America/New_York:20260310T163000 CATEGORIES:Functional Analysis Seminar SUMMARY:Todd Quinto: Spherical Radon transforms in tomography LOCATION:Kemeny 343 URL:https://math.dartmouth.edu/~funct-an/ END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cbbe@math.dartmouth.edu DTSTART;TZID=America/New_York:20260316T123000 CATEGORIES:Thesis Defence SUMMARY:Haochen Wu: Gauss composition and Orthogonal modular forms on binary lattices LOCATION:Haldeman Center 041 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cbf0@math.dartmouth.edu DTSTART;TZID=America/New_York:20260402T151500 CATEGORIES:Math Colloquium SUMMARY:Carina Curto: TBA LOCATION:TBA END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cc48@math.dartmouth.edu DTSTART;TZID=America/New_York:20260407T143000 DTEND;TZID=America/New_York:20260407T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Nathan Henry Morris: TBD LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cc62@math.dartmouth.edu DTSTART;TZID=America/New_York:20260409T151500 CATEGORIES:Math Colloquium SUMMARY:Ngoc Tran: TBA LOCATION:Kemeny 007 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cc79@math.dartmouth.edu DTSTART;TZID=America/New_York:20260421T143000 DTEND;TZID=America/New_York:20260421T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:David Urbanik: TBA LOCATION:TBA END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cc8f@math.dartmouth.edu DTSTART;TZID=America/New_York:20260428T143000 DTEND;TZID=America/New_York:20260428T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Yuta Nakayama: TBA LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cca5@math.dartmouth.edu DTSTART;TZID=America/New_York:20260430T151500 CATEGORIES:⋆ Kemeny Lecture ⋆ SUMMARY:Curt McMullen: TBA LOCATION:TBA END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351ccbc@math.dartmouth.edu DTSTART;TZID=America/New_York:20260505T143000 DTEND;TZID=America/New_York:20260505T153000 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Jerry Fu Yu: TBA LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351ccd2@math.dartmouth.edu DTSTART;TZID=America/New_York:20260507T021500 DTEND;TZID=America/New_York:20260507T031500 CATEGORIES:Algebra and Number Theory Seminar SUMMARY:Uriya First: TBA DESCRIPTION:TBA LOCATION:Kemeny 343 END:VEVENT BEGIN:VEVENT DTSTAMP:20260308T034701Z UID:20260308T03470169acf1351cceb@math.dartmouth.edu DTSTART;TZID=America/New_York:20260521T151500 DTEND;TZID=America/New_York:20260521T161500 CATEGORIES:Math Colloquium SUMMARY:Mark Sellke: TBA DESCRIPTION:TBA LOCATION:Kemeny 007 END:VEVENT END:VCALENDAR