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In his study of quadratic forms, Milnor conjectured that certain motivic cohomology groups appear as the graded pieces of the filtration by powers of the fundamental ideal on the Witt ring of symmetric bilinear forms. This conjecture was proved by Kato for fields of characteristic 2 and by Orlov–Vishik–Voevodsky and Morel for fields of other characteristics. In this talk, I will present an analogue of this conjecture for local rings that are not necessarily fields, with particular emphasis on mixed characteristic 2. As an application, over any unramified regular local ring, this produces syntomic cohomological invariants of symmetric bilinear forms.

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To study supersymmetric field theories in families and to track their behavior under dualities, physicists often realize such theories via intersecting D-branes in type II string theories. In this talk, I’ll describe how such constructions may be codified at the level of twists in terms of natural moduli problems attached to Calabi-Yau categories.

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In the course of their proof of Shuffle Theorem in algebraic combinatorics, Carlsson and Mellit introduced a remarkable algebra A_{q,t} and its cousin B_{q,t}.  Later work revealed interesting connections of the algebra B_{q,t} with the elliptic Hall algebra and parabolic Hilbert schemes of points. I will describe a generalization of B_{q,t} for an arbitrary quiver Q and outline its connections with the K-theoretic Hall algebra of Q and parabolic quiver varieties. This is a joint work with Nicolle Gonzalez and Jose Simental.

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

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The almost-commuting stack is the moduli of triples (g,X,q), where g is a group element, X is a Lie algebra element, and q is a scalar, such that g^{-1}Xg = qX. We compute the dg-algebra of G^\vee-invariant functions on the almost-commuting stack as a graded dg-algebra over k[q,1/q]. In other words, we calculate the pushforward of the structure sheaf to G_m/G_m. Away from roots of unity, this k[q,1/q]-dga agrees with O(T^\vee)^W[q,1/q], while at q = 1, there are derived corrections with nonzero grading degree. Unlike the related work of Li-Nadler-Yun on the multiplicative commuting stack, or of BenZvi-Chen-Helm-Nadler on coherent Springer theory, our approach does not require any form of Bezrukavnikov's equivalence. Instead, the primary technical input is a categorification of the Schur orthogonality relations / Hirzebruch-Riemann-Roch theorem, which is extracted from an adjointability criterion for doubly oplax-twisted topological field theories.

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I will discuss the constructions of different Nori type motivic categories and give descriptions of the different properties known till date. Then we will describe  conjectures and questions related to these categories. 

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An weight \mu is called almost dominant if its paring with all coroots is at least -1.  I will explain how to write such affine Grassmanians slices W^\lambda_\mu as a product of an affine space with a dominant affine Grassmannian slice.  There is a similar description on the quantized level as well.  This is part of a joint project with Kalmykov, Leroux-Lapierre, Pinet, Weekes.

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

RSVPs are requested for this event for in-person and Zoom attendees.
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In this talk I will try to describe how I think about AI, where it's going, and why I think mathematicians can help make it safe. I will also shamelessly advertise for the Mathematical A.I. Safety Institute (MAISI) opening in January!

"AI safety" is an umbrella term referring to any kind of intervention that will enable us to co-exist safely with a powerful AI system. People think about various kinds of interventions: What kind of AI system we build and how we train it; How do we interact with our AI systems; How do we set up our world so that AI can exist safely within it.

At the moment, the kinds of theoretical tools we have for thinking about safety are highly limited. There are intuitions for what one might want in order to make a safe AI but they are nascent and mostly pre-rigorous, which makes them hard to work with and implement. That is where theoreticians - including mathematicians - come in!

This event will be followed by a teatime reception from 3:00-3:30 p.m. open to all on-site attendees.

Speaker Bio: Jacob Tsimerman, Scientific Director of the Mathematical A. I. Safety Institute (MAISI), is a 2026 Fields Medalist and Professor at the University of Toronto. He has received the 2023 Ostrowski Prize, the 2022 New Horizons in Mathematics Prize, the 2019 Coxeter–James Prize, and the 2015 SASTRA Ramanujan Prize.

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Elliptic quantum groups are based on elliptic solutions of the
dynamical Yang-Baxter equation. I will discuss a variant, the
restricted elliptic quantum groups, in which the dynamical parameter
takes values in a finite set.  The corresponding R-matrix elements are
the Boltzmann weights of the Andrews-Baxter-Forrester Restricted
Solid-On-Solid models, describing random discrete surfaces. The
representations of these quantum groups are naturally defined on
vector spaces graded by a groupoid G. Their characters generate a
commutative algebra in the convolution algebra of G.  The quantum
group itself is a bialgebra object in the category of vector spaces
graded by the groupoid of commutative squares in G.
The talk is based on joint work with Muze Ren and with Jelena Anic.

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

Zoom Link

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

Zoom Link

Zoom Link

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This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Dwinelle Hall room 79.

In this course we will approach the theory of Yangians — quantum groups associated with loop algebras — via geometric representation theory. Key topics and constructions will include: Quantum loop groups, Nakajima quiver varieties, symplectic resolutions, RTT formalism, R matrices, BBDG decomposition theorem, cohomological Hall algebras and Borcherds algebras.

Zoom Link

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