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Events for April – August

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Wed, Apr. 1 2pm (MATH350)	Math Phys Evan Wickenden (CU Boulder Physics) Periodic Schr�dinger operators and Bloch theory II
Wed, Apr. 1 3pm (Kitt Cent…	DeLong Guoliang Yu (Texas A&M University) View Online:https://cuboulder.zoom.us/j/97834671785 X Scalar curvature plays a fundamental role in geometry and in general relativity. Motivated by this connection, Misha Gromov proposed a striking rigidity conjecture: for a convex polyhedron, one cannot simultaneously increase the scalar curvature of a Riemannian metric and the mean curvature of its faces while decreasing the dihedral angles. This rigidity principle has deep consequences, including implications for the positive mass theorem in general relativity. In this talk, I will introduce Gromov�s conjecture and explain the ideas behind its proof using Dirac operators. This is joint work with Jinmin Wang and Zhizhang Xie. I will make an effort to keep the talk accessible to graduate students and non-experts. The Dirac operators and scalar curvature rigidity of manifolds Sponsored by the Meyer Fund
Thu, Apr. 2 1pm (MATH 350)	Algebraic Geometry Multiple speakers X Spring 2026 FRAG Day FRAG Day
Thu, Apr. 2 2:10pm (MATH220)	Math Phys Jorgen Ellegaard Andersen (University of Southern Denmark) X We will consider Geometric Quantization on general K�hler phase spaces and propose a program for compatible constructions of the quantization of functions, the Hilbert space structure, and the dependence on the choice of the K�hler structure (generalized Hitchin connection), fixing only the underlying symplectic manifold and a prequantum line bundle. We will in particular see explicitly how the curvature of the phase space modifies the quantization. Geometric Quantization of General K�hler Manifolds
Fri, Apr. 3 12:20pm (Math …	Math Edu Rebecca Swanson (Colorado School of Mines) X At research institutions, faculty are tasked with coordinating core courses that are required of a large number of students. At the Colorado School of Mines, all students are required to take Calculus I, Calculus II, and Calculus III, and many students are required to a number of other courses. In this talk, I'll discuss my own experiences with coordination at the Colorado School of Mines and related research. In particular, I will share some of our current coordination practices as well as implementations of flipped learning in Calculus II (published work) and alternative grading in Calculus I (preliminary results). When Innovation Meets Coordination in Calculus
Tue, Apr. 7 11am (MATH 350)	Number Theory Yu Fu (CalTech) X A central theme in modern arithmetic geometry is to understand the distribution of special subvarieties�loci where objects acquire extra symmetry, smaller Mumford�Tate group, or atypical monodromy. Their behavior is closely tied to conjectures on unlikely intersections, and a recurring phenomenon is that these special loci, while highly structured, are notably sparse. A natural question is how one should measure this sparsity in different arithmetic contexts. In this talk, I will discuss two illustrations of this theme. The first concerns one-parameter families of abelian varieties over number fields. How often does a specialization acquire extra endomorphisms? I will explain a quantitative result showing that such �non-generic� fibers occur on a height-density zero set of rational points. The second illustration arises from the p-adic geometry of Shimura varieties. While the Hecke orbit conjecture asserts that the prime-to-p Hecke orbit of a point is Zariski dense in the central leaf containing it, one may ask how large such an orbit can be in the p-adic analytic topology. I will describe a conjectural picture�supported by new results on p-adic monodromy�suggesting that even the full Hecke orbit is p-adically nowhere dense. Sparsity Phenomena in Arithmetic Geometry
Tue, Apr. 7 1:25pm (MATH 2…	Algebra/Logic Nick Jamesson (CU Boulder) X The family of promise constraint satisfaction problems (PCSPs) is a variant of the well studied family of constraint satisfaction problems (CSPs). The computational problem of solving promise systems of equations over algebras is a variant of the problem of systems of equations over algebras. Given two algebras A and B of the same signature such that A maps homomorphically into B, one can ask if a system of equations has a solution in A or if it doesn't even have a solution in B. Given a finite algebra A, it is known that determining whether or not systems of equations over A have a solution is either solvable in polynomial time, or is NP complete (the famous dichotomy theorem for CSPs.) The question of whether or not a dichotomy holds for promise systems of equations over finite algebras is open in general. I will present some dichotomy results for promise systems of equations over various classes of algebras, including Mal'cev algebras. Promise Systems Of Equations Over Finite Algebras
Tue, Apr. 7 2:30pm (MATH 3…	Lie Theory J. Carlos Mart�nez Mori (University of Colorado Denver) X We show that the number of zero dinv Fubini rankings with n competitors and at most l + 1 ties at any rank is given by the maximum number of regions of an l-dimensional cake with n-1 cuts. This is joint work with Pamela E. Harris and Alexander N. Wilson. Zero Dinv Fubini Rankings and Cake-Cutting Geometry
Wed, Apr. 8 2:10pm (MATH 3…	Math Phys Scott Maccarone (CU Boulder) Kato's theorem on the selfadjointness of the molecular Hamiltonian
Thu, Apr. 9 1:30pm (MATH 3…	Topology Jean-Paul Brasselet (CNRS) X When he built his tower, Gustave Eiffel engraved the names of 72 French scientists, all men. Recently, it has been decided to engrave the names of 72 French women scientists on the tower. Eleven mathematicians were selected, including Marie-H�l�ne Schwartz. One of her major works, in 1965, was the construction of characteristic classes for singular complex analytic varieties. This result was subsequently part of a conjecture by Grothendieck and Deligne, proved by Robert MacPherson. The classes are now called "Schwartz-MacPherson classes.� The elementary presentation will focus as much on the life of Marie-H�l�ne Schwartz as on her proof of the Poincar�-Hopf Theorem for singular varieties.� That is a join work with Thuy Nguyen (UNESP, Rio Preto, Brazil) and Tadeusz Mostowski (Warsaw, Poland). Joint with Math Physics Seminar and CTQM Marie-H�l�ne Schwartz, a name on the Eiffel tower
Thu, Apr. 9 1:30pm (Math350)	Math Phys Jean-Paul Brasselet (CNRS, Marseille) X When he built his tower, Gustave Eiffel engraved the names of 72 French scientists, all men. Recently, it has been decided to engrave the names of 72 French women scientists on the tower. Eleven mathematicians were selected, including Marie-H�l�ne Schwartz. One of her major works, in 1965, was the construction of characteristic classes for singular complex analytic varieties. This result was subsequently part of a conjecture by Grothendieck and Deligne, proved by Robert MacPherson. The classes are now called "Schwartz-MacPherson classes. The elementary presentation will focus as much on the life of Marie-H�l�ne Schwartz as on her proof of the Poincar�-Hopf Theorem for singular varieties. That is a join work with Thuy Nguyen (UNESP, Rio Preto, Brazil) and Tadeusz Mostowski (Warsaw, Poland). Joint with Topology Seminar and CTQM Marie-H�l�ne Schwartz, a name on the Eiffel tower Sponsored by the Meyer Fund
Fri, Apr. 10 9am (JILA Audi…	Math Phys Martin Schottenloher (TU Munich) X Link to PDF abstract https://drive.google.com/file/d/1g3eW-mgXx6HA4sX61rQcrIaVFK7L0Xc1/view Joint with Topology Seminar and the CTQM Geometric Quantization: A mathematical path to quantum models Sponsored by the Meyer Fund
Fri, Apr. 10 10:10am (JILA …	Math Phys Hessel Posthuma (University of Amsterdam) X I�ll start by giving an introduction to index theory in the presence of symmetries and explain how this fits into the framework of noncommutative geometry. After that I will focus on the case of proper actions of groups and explain a recent "higher fixed point formula" obtained in joint work with Paolo Piazza, Yanli Song and Xiang Tang. Joint with Topology Seminar and the CTQM Higher index theory for proper actions Sponsored by the Meyer Fund
Fri, Apr. 10 11:10am (JILA …	Math Phys Marvin Qi (Kadanoff Center for Theoretical Physics) X Symmetries and anomalies provide powerful constraints on the dynamics of quantum many-body systems. In this talk, I will revisit a class of models known as quantum dimer models, and argue for the presence of a mixed anomaly involving lattice rotations and a higher-form symmetry. This anomaly forbids the existence of any symmetry preserving gapped phase, consistent with the known phase diagrams of these models. This talk is based on work in progress with Wilbur Shirley and Clay C�rdova. Joint with Topology Seminar and the CTQM Lattice anomalies in quantum dimer models Sponsored by the National Science Foundation
Fri, Apr. 10 11:40am (JILA …	Math Phys Laura Shou (University of Maryland) X Joint with Topology Seminar and the CTQM Exactly solvable topological phase transition in a quantum dimer model Sponsored by the National Science Foundation
Fri, Apr. 10 12:20pm (Math …	Math Edu Rebecah Deans X A large part of mathematical maturity is being able to communicate a solution to a problem clearly, as well as being able to justify to a�reader that the proposed solution is correct. �Even so, good communication is generally not emphasized in high school and undergraduate mathematics instruction, leaving assessment of student comprehension largely up to the instructor's interpretation. In this talk, I will discuss how MATH 2400 has attempted to improve student communication on free response exam questions by introducing a communication component to free response rubrics. I will also discuss how we have attempted to prepare both students and instructors for this new aspect of assessment. Improving and Assessing Student Communication in Coordinated Courses
Fri, Apr. 10 12:30pm (JILA …	Math Phys Anton Kapustin (California Institute of Technology) X It is expected that a generic closed many-body system prepared in a well-behaved initial state will eventually thermalize, i.e. approach a Gibbs state. This property, while compatible with and even demanded by the physical intuition, is much stronger than ergodicity or mixing and is difficult to justify mathematically. Similarly, a generic many-body system subject to a periodic drive (a Floquet system) is expected to heat up and approach the state of maximal entropy. In this talk I will describe an infinite set of many-body Floquet systems of algebraic origin, both classical and quantum, for which thermalization of very general initial states can be studied analytically as well as numerically. Joint with Topology Seminar and the CTQM Thermalization and chaos in many-body quantum and classical dynamical systems of algebraic origin
Fri, Apr. 10 2:10pm (JILA …	Math Phys David Jonas (CU Boulder) X The Born-Oppenheimer or adiabatic approximation separates fast electronic dynamics from slow nuclear dynamics. In this approximation, the electronic Schr�dinger equation is solved for fixed nuclei and then each electronic energy is used as a potential energy surface for solving the vibrational Schr�dinger equation. Von Neuman and Wigner put forth a dimensional argument that the potential curves should avoid each other in diatomic molecules but that potential surfaces should have intersections in polyatomic molecules. With the local shape of a double-cone in 2D, these conical intersections have been identified by their associated topological phase (Berry phase) and are now known to occur in many photochemical reactions. Nevertheless, they are features of an approximation. Several years ago, we were exploring a non-adiabatic model for energy transfer in photosynthesis and found that the exact non-adiabatic eigenfunctions have a weird nodal structure that parallels the dimensional arguments of Von Neuman and Wigner. Instead of the usual nodal points in 1D, nodal curves in 2D, etc. the nonadiabatic eigenfunctions have avoided nodes in 1D, point nodes in 2D, etc. In the neighborhood of a point node in 2D, the nonadiabatic eigenfunctions have the local shape of a cone. High symmetry can generate higher order nodes. The nodes have a signed integer electronic index that measures electronic state vector rotation around a closed vibrational path and is locally stable to perturbations. I will discuss examples of conical nodes that occur by accident and near symmetry-required conical intersections. M. Born, Gott. Nachr. math. phys. Kl. 6, 1 (1951). J. von Neumann and E. Wigner, Phys. Z. 30, 467 (1929). M. V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984). M. Klessinger and J. Michl, Excited States and Photochemistry of Organic Molecules. (VCH Publishers, New York, 1995). V. Tiwari, W. K. Peters and D. M. Jonas, Proc. Natl. Acad. Sci. USA 110, 1203 (2013). P. W. Foster, W. K. Peters and D. M. Jonas, Chem. Phys. Lett. 683, 268 (2017). P. W. Foster and D. M. Jonas, J. Phys. Chem. A 121, 7401 (2017); 123, 1273 (2019). P. W. Foster and D. M. Jonas, Chem. Phys. 520, 108 (2019). Joint with Topology Seminar and the CTQM The weird geometry of non-adiabatic eigenfunctions
Fri, Apr. 10 3:35pm (DUANE …	Math Phys Daniel Spiegel (Harvard Center of Mathematical Sciences and Applications) X Matrix product states form an especially tractable and well-understood class of states of quantum spin chains. In particular, when working with matrix product states, one obtains elegant derivations of various topological indices that classify phases of both symmetry protected states as well as continuously parametrized families of states. I will begin this talk with a brief introduction to matrix product states on infinite lattices, move on to discuss joint work with my CU Boulder colleagues on the homotopy type of the space of matrix product states, and finally I will mention work in progress on the classification of matrix product states that are both symmetry-protected and parametrized. Joint with Topology Seminar and the CTQM Parametrized Families of Matrix Product States Sponsored by the Meyer Fund
Fri, Apr. 10 4:40pm (DUANE …	Math Phys Xiang Tang (Washington St Louis) X Let G be a connected linear real reductive group with a maximal compact subgroup K. In this talk, we will discuss an approach to studying the large-time behavior of the heat kernel on the corresponding homogeneous space G/K using Bismut's formula. We will try to explain how Bismut's formula provides a natural link between the index theory and representation theory. In particular, Vogan's lambda-map in the representation theory of G plays a central role in the large time asymptotic analysis about the trace of the heat kernel. This talk is based on joint works with Shu Shen and Yanli Song. Joint with Topology Seminar and the CTQM The large time behavior of the heat kernel on homogenous spaces and Bismut's formula Sponsored by the Meyer Fund
Sat, Apr. 11 9am (JILA Aud…	Math Phys Emil Prodan (Emil Prodan) X I will describe how to deal with single-particle dynamics over complex aperiodic discrete geometries using C-algebras. Using numerical examples, I will first convey that any local Hamiltonian over such a geometry falls into one and same algebra, completely determined by the underlying discrete geometry. I will then describe this algebra based on the notion of phason spaces, and compute it for particular cases (e.g. twisted bilayers). K-theory of this algebra tells us what topological invariants are available for a given discrete geometric structure. For example, a twisted bilayer can host up to second-Chern numbers but nothing above that. The punch line of the talk would be a C-formulation of ordinary and higher order bulk-defect correspondences. The claim is that, given a geometry with defects (surfaces, hinges, corners, dislocations, disclinations, etc), the C-algebraic framework supplies a device to enumerate all possible non-trivial defect-boundary correspondences, without missing one. I will include numerical demonstrations of these principles. References: P. D. Ojito, E. Prodan, T. Stoiber, C-framework for higher-order bulk-boundary correspondences, Comm. Math. Phys 406, 233 (2025). B. Mesland, E. Prodan, Classifying the dynamics of architected materials by groupoid methods, Journal of Geometry and Physics 196, 105059 (2024). Joint with Topology Seminar and the CTQM Taming Spatial Complexity in Topological Dynamics with C*-Algebras
Sat, Apr. 11 10:10am (JILA …	Math Phys Henri Moscovici (Ohio State University) X My talk centers on an �ordinary-looking� ordinary differential equation�the prolate spheroidal wave operator�which has played a surprisingly rich and unexpected role across several fields. It first arose as a �lucky accident� in the 1960s solution by Slepian, Landau, and Pollak of the problem of time-and band-limiting of signals, raised by Claude Shannon. The same operator reappeared in the late 1990s through a cutoff mechanism in Alain Connes� trace formula reformulation of the Weil explicit formula in number theory. More recently, in joint work with Connes (2022), we found that when this operator is extended from a finite interval to the whole line, its spectrum reproduces�with striking accuracy�the squares of the imaginary parts of the zeros of the Riemann zeta function. I will conclude with a refinement of this phenomenon based on analyzing the operator in the complex domain. Joint with Topology Seminar and the CTQM The unlikely bond between the prolate wave operator and Riemann�s zeta function Sponsored by the Meyer Fund
Sat, Apr. 11 11:10am (JILA …	Math Phys Nikita Sopenko (Institute for Advanced Studies) X Gapped phases of two-dimensional free-fermionic systems without any symmetry are classified by an integer-valued topological invariant called the Chern number, which counts the net chirality of boundary modes. It has long been conjectured that systems with distinct Chern numbers cannot be deformed into each other without a phase transition, even in the presence of arbitrarily strong interactions. In this talk, I will present a construction of a many-body index that generalizes the Chern number to the interacting setting and allows us to prove this conjecture. When the edge modes can be described by a conformal field theory, the index provides a microscopic characterization of the chiral central charge. Joint with Topology Seminar and the CTQM A many-body index for 2d topological superconductors Sponsored by the National Science Foundation
Sat, Apr. 11 11:40am (JILA …	Math Phys Michael Hermele (CU Boulder) X There are now many examples of gapped fracton models, which are defined by the presence of restricted-mobility excitations above the quantum ground state. This complex landscape of examples is far from being mapped out. In this talk, I will describe recent progress on characterization and classification of fracton orders, and on related problems for subsystem symmetries. Joint with Topology Seminar and the CTQM Navigating the Fracton Landscape
Tue, Apr. 14 1:25pm (MATH 2…	Algebra/Logic Sangman Lee (CU Boulder) X We study the subpower intersection problem (SIP) for a fixed finite semigroup S: given sets A,B of n-tuples A,B� over S, decide whether the subsemigroups generated by A and B have nonempty intersection. We will present the following complexity results for SIP over finite semigroups. For every finite semigroup S, SIP(S) is in PSPACE. For finite bands, SIP(S) is in P if S is normal and is NP-complete otherwise. For full transformation semigroups T_n, SIP(T_2) is NP-complete and SIP(T_n) is PSPACE-complete for n > 2. For finite (completely) simple semigroups, SIP(S) is in P, and moreover SIP(S^1) is in P if S is a group and is NP-complete otherwise. The subpower intersection problem for finite semigroups
Wed, Apr. 15 12:20pm (MATH …	Diversity Facilitators: Howy Jordan, Emily Montelius, and Maya Ornstein X The CHAT+ will start at 12:20. Lunch will be available at 12:00. If you plan to join, we ask that you RSVP by April 12 at the link below. There is also an option to indicate any dietary restrictions we should keep in mind. https://docs.google.com/forms/d/e/1FAIpQLSf_G3REEmhuvZwpPXpsZI-xF8UhZpRa8yfx--fjS-iigv31AQ/viewform?usp=sharing&ouid=102614817914920289902 Supporting Minority Students in Graduate Programs
Wed, Apr. 15 2:10pm (Math350)	Math Phys Saksham Hassanandani (CU Boulder) The Bargmann-Segal representation and Schr�dinger operators
Fri, Apr. 17 2:30pm (MATH 3…	PDE/Analysis Irina Holmes Fay (University of Wyoming) X We investigate weak-type (1,1) boundedness of sparse operators with respect to Lebesgue measure. Specifically, we find the Bellman function maximizing level sets of sparse operators (localized to an interval) and use this to find the exact weak-(1,1) norm of these sparse operators. The Bellman Function for Level Sets of Sparse Operators Sponsored by the Meyer Fund
Tue, Apr. 21 1:25pm (online)	Algebra/Logic Jakub Rydval (TU Wien) View Online:https://cuboulder.zoom.us/j/96896272260 X In 2008, Bodirsky and Grohe showed that for every \Pi_n^P-level of the Polynomial Hierarchy (PH) there are omega-categorical Constraint Satisfaction Problems (CSPs) complete for this level. We show that, in fact, there are omega-categorical CSPs complete for any level of the PH. To this end, we use a recent result of Bodirsky, Kn\"{a}uer, and Rudolph for constructing omega-categorical CSPs from sentences of Monadic Second-Order logic (MSO) with certain preservation properties. As a secondary contribution, we develop a new tool for producing MSO sentences satisfying said preservation properties. In the present talk, I give an overview of the above-mentioned results and motivate several new questions. This is joint work with Santiago Guzman-Pro. The polynomial hierarchy and omega-categorical CSPs
Tue, Apr. 21 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X A pair (g,k) of Lie algebras is a symmetric pair if k is the set of fixed points of an automorphism of g of order 2. We will show that when g and k are simply laced Lie algebras of equal rank, the pair gives rise to some combinatorial structures whose numerical invariants can be predicted in terms of matroids that are representable over the field with two elements. This is based on joint work with Tianyuan Xu (University of Richmond). Symmetric pairs and binary matroids
Wed, Apr. 22 2:10pm (Math350)	Math Phys Mudassir Moosa (CU Boulder Physics) X The AdS/CFT correspondence establishes a duality between a gravitational theory in an Anti-de Sitter (AdS) spacetime and a conformal quantum field theory on the boundary of the spacetime. This has led to the notion that the spacetime is an emergent concept, but how it emerges from quantum theory on a boundary is not fully understood. In this talk, I will discuss some work in this direction using the theory of von Neumann algebras. Specifically, I will consider a (non-local) conformal Generalized Free Field theory dual to a local scalar field theory in AdS_2 spacetime and will explore the properties of the modular flow and modular conjugation of "time-interval algebras". I will show that these algebras satisfy "Holographic Algebraic Properties". Moreover, I will prove the converse statement that the existence of Holographic Algebraic Properties in any quantum system implies a local QFT in an AdS_2 spacetime. This explains the emergence of a local spacetime in a simple setup. von Neumann Algebras in Holography and Emergence of Spacetime
Thu, Apr. 23 2:30pm (MATH 3…	Functional Analysis J. Quigg (Arizona State University) X One approach to identifying the C*-algebra of a product system over N^k is to build a representation of it with the aim of applying the Gauge-Invariant Uniqueness theorem. The main problem is how to build the representation. This is complicated by the commutativity of N^k - so many balanced tensor-product correspondences are isomorphic. I'll show how an abstract categorical result of Fowler-Sims can be used to surmount this obstacle. Joint work with Valentin Deaconu, Menevse Eryuzlu Paulovicks, and S. Kaliszewski. Use of monoidal categories to generate representations of product systems over N^k Sponsored by the Meyer Fund
Thu, Apr. 23 11pm (MATH 220)	Functional Analysis Roberto Hernandez Palomares (University of Waterloo) X Spin models for singly-generated Yang-Baxter planar algebras are known to be determined by certain highly-regular classical graphs such as the pentagon or the Higman-Sims graph, which are extremely rare. Examples of spin models include the Jones and Kauffman polynomials. We will discuss the notion of higher-regularity for quantum graphs and give new examples of non-classical graphs yielding spin models. Time allowing, we will discuss some applications to quantum groups, topology and quantum information. Quantum graphs and spin models Sponsored by the Meyer Fund
Fri, Apr. 24 2:30pm (MATH 3…	PDE/Analysis Xueying Yu (Oregon State University) X This talk focuses on a fundamental concept in the field of partial differential equations - unique continuation principles. Such a principle describes the propagation of the zeros of solutions to PDEs. Specifically, it answers the question: what condition is required to guarantee that if a solution to a PDE vanishes on a certain subset of the spatial domain, then it must also vanish on a larger subset of the domain. Motivated by Hardy�s uncertainty principle, Escauriaza, Kenig, Ponce, and Vega were able to show in a series of papers that if a linear Schr�dinger solution decays sufficiently fast at two different times, the solution must be trivial. In this talk, we will discuss unique continuation properties of solutions to higher-order Schr�dinger equations and variable-coefficient Schr�dinger equations, and extend the classical Escauriaza-Kenig-Ponce-Vega type of result to these models. This is based on joint works with S. Federico-Z. Li, and Z. Lee. Some unique continuation results for Schr�dinger equations Sponsored by the Meyer Fund
Wed, Apr. 29 2:10pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M) X In this pedagogical talk, we will discuss a simple setting in which to explore the methods we saw in Evan Wickenden's talk earlier this semester: discrete Schrodinger operators (1d periodic). We will compare the two methods that were introduced: the Floquet discriminant and the Bloch transform. In the 1d periodic case, there are some patterns predicted by Hill's theorem which can be disturbed by a suitably strong perturbation of the operator. The latter observation is related to some ideas of spectral engineering: resonant gap opening and flat bands. We will not present any research results, although some numerical simulation we will see may lead to a research project. Explorations of periodic Schrodinger operator
Mon, May. 11 2pm (MATH 350)	Algebra/Logic Michael Pinsker (TU Wien) X For a permutation group G on a set X, a mixed identity is an expression of the form w(x_1,...,x_n,g_1,...,g_m)=1, where w is a word in the language of groups with constants g_1,...,g_m from G and free variables x_1,...,x_n. We say that the mixed identity holds in G if substitution of arbitrary elements of G for the free variables yields a true statement. The mixed identity is singular if deletion of all constants yields a true statement in the free group: for example, xgx^{-1}=1 (where x is a variable and g a constant) is singular. We consider the question which non-singular mixed identities hold in a given group G. The group G is oligomorphic if it acts with finitely many orbits on X^n, for all n. Based on several examples, Bodirsky, Schneider, and Thom have conjectured that in oligomorphic groups only singular identities can hold. We confirm this conjecture for all oligomorphic G without algebraicity, i.e. with the property that for any tuple t of elements of X, the stabilizer of t in G does not stabilize any element outside t. In fact, we obtain this result under even more general conditions satisfied e.g. by the general linear group of any infinite vector space over a finite field. This is joint work with Paolo Marimon (Oxford). Mixed identities in oligomorphic groups Sponsored by the Meyer Fund
Mon, May. 11 3pm (MATH 350)	Algebra/Logic Andrei Bulatov (Simon Fraser University) X We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($\AutCSP$) where constraint languages and instances are specified by finite automata. The $\AutCSP$ captures infinite yet finitely describable sets of relations, enabling concise representations of complex constraints. Studying the complexity of the $\AutCSP$s illustrates the interplay between classical CSPs, automata, and logic, sharpening the boundary between tractable and intractable constraints. We show that checking whether an operation is a polymorphism of such a language can be done in polynomial time. Building on this, we establish several complexity classification results for the $\AutCSP$. In particular, we prove that Schaefer’s Dichotomy Theorem extends to the $\AutCSP$ over the Boolean domain, and we provide algorithms that decide tractability of some classes of $\AutCSP$s over arbitrary finite domains via automatic polymorphisms. An important part of our work is that our polynomial-time algorithms run on $\AutCSP$ instances that can be exponentially more succinct than their standard CSP counterparts. Automatic constraint satisfaction problem Sponsored by the Meyer Fund

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