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Events for May – September

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Thu, May. 1 12:30pm (Online)	Rep Theory Juan Villarreal (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk we introduce a canonical decreasing filtration on intertwiners of a vertex algebra. We study the associated graded spaces. Then, we define Poisson vertex intertwiners and Poisson intertwiners. We obtain relations between the associated varieties of modules of a vertex algebra. Intertwiners and filtrations
Thu, May. 1 2:30pm (MATH 3…	Functional Analysis David Blecher (University of Houston) X Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in modern analysis and also in modern quantum physics (such as quantum information theory). They have an extensive theory, and have very important applications in all of these subjects. We present recent work (2025) on the real case of the theory of (complex) operator systems, and also the real case of their remarkable tensor product theory, due in the complex case to Paulsen and his coauthors and students, building on pioneering earlier work of Kirchberg and others. We uncover several notable differences between the real and complex theory, including the absence of minimal and maximal functors in the category of real operator systems. We show how this is related to entanglement. We also develop very many foundational structural results for real operator systems, and elucidate how the complexification interacts with the basic constructions in the subject. We give the real analogues of the Kirchberg conjectures (and of several important related problems that have attracted much interest recently such as the Tsirelson problem on quantum correlations), and the deep relationships between them. Joint work with Travis Russell. Real operator systems
Wed, May. 7 3:30pm (Math350)	Math Phys Andrew Hamilton (CU Boulder Astrophysics) X String theory offers a viable theory of quantum gravity, with spin 2 gravitons encoded in closed strings. But the failure to find evidence for supersymmetry at the LHC has left string theory in disarray. A solution to the problem is in plain sight: revert to old-fashioned, 1970s-style, nonsupersymmetric, bosonic string theory, reenvisaged as a theory of all the forces, not just the strong force. The old theory correctly reproduces the Brauer-Weyl (1935) algebraic relation between fermions and bosons seen in the standard model, whereas supersymmetry does not. Sages of string theory commonly reject bosonic string theory on the grounds that (1) it does not admit fermions, and (2) its ground state is tachyonic. But rejection (1) assumes that fermions are strings, wheres the fermions of bosonic string theory are the endpoints of strings, and are not themselves strings; in modern parlance, the fermions are excitations of the D-brane boundary of strings. As to rejection (2), the properties of the tachyon are precisely those of a Higgs field: it is a multiplet of the unbroken symmetry; the "vacuum" state where the Higgs field vanishes identically is tachyonically unstable; and it has spin zero. I propose Clifford(11,1) string theory, a 26-dimensional, tachyonic, bosonic, open string theory, whose bosons occupy all 26 dimensions while their fermionic endpoints are confined to an 11+1 dimensional D-brane. The 26 dimensions compactify to 12 on the 14-dimensional self-dual torus of the rank 14 SU(8)xSU(8) subgroup of the group G^2(10)=U(16) generated by Clifford(11,1) multivectors of grade 2 (mod 4). Clifford(11,1) string theory
Wed, May. 14 3:30pm (MATH 2…	Math Phys Noah Song (CU Boulder) X TBA Coupled Cluster Theory
Thu, May. 22 9am (Online)	Rep Theory Hao Zhang (Tsinghua University) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) -cofinite VOA . This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707, 2503.23995) joint with Bin Gui. The sewing-factorization theorem for C_2-cofinite VOAs
Thu, Jun. 5 3:30pm (MATH 3…	Functional Analysis PIOTR M. HAJAC (IMPAN, Warsaw, Poland) X Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphims. As both functors are often used at the same time, one needs a new category of graphs that allows a “common denominator” functor unifying the covariant and contravariant constructions. In this talk, I will show how to solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. I will illustrate relation morphisms of graphs by many naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. Although I will focus on Leavitt path algebras and graph C-algebras, time permitting, I will unravel functors given by path algebras, Cohn path algebras and Toeplitz graph C-algebras from suitable subcategories of RG to k-Alg. Based on joint work with Gilles G. de Castro and Francesco D'Andrea. RELATION MORPHISMS OF DIRECTED GRAPHS
Fri, Jun. 6 2:30pm (Math 2…	Noncomm Geometry Paul Bressler (Universidad de los Andes) X I will describe a construction of a complex associated to a Lie algebroid originally due to V. Schechtman and use it to obtain interesting representatives of a characteristic classes of manifolds. Characteristic classes of natural bundles Sponsored by the Meyer Fund

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