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Events for the weeks of September 8th – 20th

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Tue, Sep. 10 1:25pm (MATH 2…	Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X My goal will be to explain why a locally finite variety V has the property that its finitely generated projective algebras are free if and only if (1) the finite, nontrivial members of V are E-minimal and (2) if V has a pseudoconstant term, then V also has a constant term. Locally finite varieties whose finitely generated projectives are free
Tue, Sep. 10 2:30pm (MATH 3…	Lie Theory faculty organizers X We give an introduction to the faculty of the seminar and their research areas. ALT seminar open house
Tue, Sep. 10 3:30pm (MATH 3…	Topology Faculty Open House
Wed, Sep. 11 3:30pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M University) X The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises in diverse areas of mathematical physics. Among the particular motivations for this talk are the Floquet-Bloch decomposition of the Schrödinger operator on a periodic structure, nodal count statistics of eigenfunctions of quantum graphs, conical points in potential energy surfaces in quantum chemistry and the minimal spectral partitions of domains. In each of these problems one seeks to identify and/or count the critical points of the eigenvalue with a given label (say, the third lowest) over the parameter space which is often known and simple, such as a torus. Classical Morse theory is a set of tools connecting the number of critical points of a smooth function on a manifold to the topological invariants of this manifold. However, the eigenvalues are not smooth due to presence of eigenvalue multiplicities or ``diabolical points''. We rectify this problem for eigenvalues of generic families of finite-dimensional operators. The ``diabolical contribution'' to the ``Morse indices'' of the problematic points turns out to be universal: it depends only on the multiplicity and the relative position of the eigenvalue of interest and not on the particulars of the operator family. Using tools such as Clarke subdifferential and stratified Morse theory of Goresky--MacPherson, we express the ``diabolical contribution'' in terms of homology of Grassmannians of ppropriate dimensions. Based on a joint work with Igor Zelenko (TAMU). Berkolaiko, G., Zelenko, I. Morse inequalities for ordered eigenvalues of generic self-adjoint families. Invent. math. (2024). Morse theory for eigenvalues of self-adjoint families
Wed, Sep. 11 4:45pm (MATH 3…	Grad Student Seminar Daniel Lyness (CU Boulder) X Pending Cohomology, Duality and Eduroam
Thu, Sep. 12 11:15am (MATH …	Algebraic Geometry Adrian Neff X Given a nodal genus one curve and a proper subcurve of genus one, we will construct a contraction that collapses the subcurve to a genus one singularity. We will do this by first introducing residues for curves over local artinian rings and "twists" of these residues by tropical data from the curve, then we will use these residues to explicitly construct the contraction. Residues and contractions of genus one curves
Thu, Sep. 12 12:30pm (MATH …	Kempner Dr. Pamela E. Harris (University of Wisconsin-Milwaukee) X What is mathematical research? How does a mathematician find problems to work on? How does one build mathematical collaborations? In this talk, I will share my journey to research mathematics, what it entails, how I have developed new research ideas, and how I have found my place within the mathematical community. Mathematical topics of discussion will include lattice point visibility, parking functions, and a connection between vector partition functions and juggling. No prior mathematical background on these topics is expected nor assumed as we will introduce all the needed concepts from first principles. All that is needed is the willingness to wonder and ask the question: “what happens if…? How to choose your own mathematical adventures
Thu, Sep. 12 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce some of the basic ideas involved in the Baum-Connes conjecture. Also, this will be an organizational meeting where we plan the other talks on this subject. We will be following https://arxiv.org/abs/1703.10912. The Baum-Connes conjecture
Thu, Sep. 12 3:35pm (MATH 3…	Probability Janos, Kyle & Sean (CU Boulder) X Janos, Kyle and Sean will talk about their current research and what it's like to work in the probability group. The talks will be informal and there will be plenty of time for questions. Probability Open House
Mon, Sep. 16 4:45pm (MATH 3…	Grad Student Seminar Ezzeddine El Sai (CU Boulder) X The Yang–Mills existence and mass gap problem is one of the Millennium Prize problems and a central problem in mathematical physics. In this talk, we will discuss the statement of the problem and unravel what it means. We will also discuss connections with geometry, analysis, and probability. The Yang–Mills existence and mass gap
Tue, Sep. 17 1:25pm (MATH 2…	Algebra/Logic Nik Ruskuc (University of St Andrews) View Online:https://cuboulder.zoom.us/j/96896272260 X The height of a (finite) lattice L is the size of a maximum chain in L. Cameron, Solomon and Turull (1989) showed that the height of the subgroup lattice of the symmetric group S_n is given by \lceil 3n/2 \rceil - b(n), where b(n) is the number of 1s in the binary expansion of n. The analogue of S_n for semigroups is the full transformation semigroup T_n. Cameron, Gadoleau, Mitchell and Perese (2017) established an accurate asymptotic formula for the height of the subsemigroup lattice of T_n. But the subgroup lattice of a group G can be viewed from a different angle: it is (isomorphic to) the lattice of right (or left) congruences of G.(And one-sided congruences of a monoid are in a 1-1 correspondence with cyclic transformation representations of S.) In this talk I will introduce a general method which gives a lower bound for the height of the lattices of one- or two-sided congruences of an arbitrary semigroup, and under certain additional conditions gives the exact values. I will apply this theory to obtain the height for the lattices of right and left congruences of T_n, as well as for many other natural semigroups of transformations, partitions and matrices. This is joint work with Matthew Brookes, James East, Craig Miller and James Mitchell. Heights of congruence lattices of semigroups Sponsored by the Meyer Fund
Tue, Sep. 17 2:30pm (MATH 3…	Lie Theory Spencer Daugherty (CU) X TBA TBA
Tue, Sep. 17 3:30pm (MATH 3…	Topology Taylor Rogers An Introduction to Chromatic Homotopy Theory I
Wed, Sep. 18 3:30pm (Math350)	Math Phys Andrew Waldron (University of California at Davis) TBA Sponsored by the Meyer Fund
Thu, Sep. 19 11:15am (MATH …	Algebraic Geometry Jonathan Wise TBA
Thu, Sep. 19 2:30pm (MATH 3…	Functional Analysis Frederic Latremoliere (Denver University) TBA
Thu, Sep. 19 3:35pm (MATH 3…	Probability Mei Yin (University of Denver) TBA

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