Talks and Trips

2025

1. Conference Talk

   TBA

   Representations, Moduli and Duality. EPFL, Lausanne, Switzerland, Aug 2025

   Abs WEBSITE

   TBA

2. Conference Talk

   TBA

   Current trends in Calabi-Yau moduli. Université de Strasbourg, France, Jun 2025

   Abs WEBSITE

   TBA

3. Research Visit

   Université de Strasbourg, France, Jun 2025

   2-week visit
4. Departmental Seminar

   Cohomological Hall algebras of 1-dimensional sheaves and Yangians

   The Hong Kong University of Science and Technology, China, Mar 2025

   Abs

   The first part of this talk provides a brief and gentle introduction to the theory of 2-dimensional cohomological Hall algebras. The second part focuses on the introduction of the nilpotent cohomological Hall algebra COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S set-theoretically supported on a closed subscheme Z. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) via the Yangian of the corresponding affine ADE quiver. (joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.)

5. Research Visit

   Kavli IPMU, the University of Tokyo, Japan, Feb 2025

   6-week visit
6. Departmental Seminar

   Yangians and cohomological Hall algebras

   MALGA Seminar. Università di Padova and Università di Verona, Italy, Feb 2025

   Abs PDF

   After a brief introduction to the theory of (2-dimensional) cohomological Hall algebras of quivers, curves, and surfaces, I will discuss the cohomological Hall algebra COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S set-theoretically supported on a closed subscheme Z. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) via the Yangian of the corresponding affine ADE quiver. (joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.)

2024

1. Conference Talk

   Cohomological Hall algebras, their representations, and Nakajima operators

   Enumerative Geometry in East Asia 2024. KIAS, Korea, Dec 2024

   Abs WEBSITE PDF

   In the first part of the talk, I will provide an overview of the theory of 2d cohomological Hall algebras (COHAs), focusing on the example of COHAs arising from zero-dimensional sheaves on smooth surfaces. I will also describe certain geometric representations of these COHAs and introduce Nakajima-type operators. In the second part, I will discuss a generalization and categorification of this framework. The talk is based on joint work with Diaconescu and Porta, as well as with Diaconescu, Porta, and Yu Zhao.

2. Departmental Seminar

   Cohomological Hall algebras, their representations, and Nakajima operators

   M-Seminar. Kansas State University, USA, Nov 2024

   Abs PDF Video

   In the first part of the talk, I will briefly introduce the theory of 2d cohomological Hall algebras (COHAs), focusing on the example of COHAs arising from zero-dimensional sheaves on smooth surfaces. I will also describe certain geometric representations of these COHAs and introduce Nakajima-type operators. In the second part, I will discuss a generalization and categorification of this framework.

3. Conference Talk

   Yangians and cohomological Hall algebras

   Workshop on Representation Theory and Mathematical Physics. New Perspectives on Yangians and Quantum Affine Algebras. Università di Parma, Italy, Oct 2024

   Abs WEBSITE PDF

   In this talk, I will introduce a conjectural “new” half of the affine Yangian of type ADE and explain how it arises naturally from the theory of cohomological Hall algebras.

4. Conference Talk

   Cohomological Hall algebras, quantum groups, and their categorification

   Hopf Algebras and Monoidal Categories. Università di Ferrara, Italy, Sep 2024

   Abs WEBSITE PDF

   The present talk serves as a gentle introduction to the theory of cohomological Hall algebras and its connection to quantum groups. If time allows, it will also discuss an approach to the categorification of quantum groups through categorified Hall algebras.

5. Conference Talk

   From four-dimensional gauge theories to cohomological Hall algebras, and back

   Algebraic structures in gauge theory and geometry. Lorentz Center, Leiden, The Netherlands, Jul 2024

   WEBSITE PDF
6. Conference Talk

   From AGT Conjecture to Cohomological Hall Algebras

   Program “BPS Dynamics and Quantum Mathematics”. The Galileo Galilei Institute for Theoretical Physics, Firenze, Italy, Jun 2024

   PDF Video
7. Departmental Seminar

   Cohomological Hall algebras, their representations, and Nakajima operators

   ICTP, Italy, May 2024

   PDF
8. Departmental Seminar

   Cohomological Hall algebras and their representations, versus Nakajima operators

   MIT, USA, Apr 2024

   PDF
9. Research Visit

   MIT, USA, Apr 2024

   2-week visit
10. Departmental Seminar

    Categorified Hall algebras and their representations, versus categorified Nakajima operators

    Kavli IPMU, Japan, Mar 2024

    PDF
11. Research Visit

    Kavli IPMU, the University of Tokyo, Japan, Mar 2024

    5-week visit

2023

1. Conference Talk

   Cohomological Hall algebras and affine Yangians

   Categorified Enumerative Geometry and Representation Theory. EPFL, Lausanne, Switzerland, Sep 2023

   Abs WEBSITE PDF

   After a brief introduction to the theory of (2-dimensional) cohomological Hall algebras of quivers, curves, and surfaces, I will discuss the cohomological Hall algebra COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S set-theoretically supported on a closed subscheme Z. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) via the Yangian of the corresponding affine ADE quiver. (joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.)

2. Conference Talk

   Categorified Hall algebras and their representations

   Motives in moduli and representation theory. Radboud University Nijmegen, The Netherlands, Jul 2023

   Abs WEBSITE PDF

   Cohomological Hall algebras play a preeminent role in the theory of moduli spaces, representation theory, and gauge theory. After a gentle introduction to the theory of two-dimensional cohomological Hall algebras and their relation to algebraic geometry and representation theory, I will describe their "categorification", called categorified Hall algebras. The second part of the talk is devoted to the introduction of representations of categorified Hall algebras via torsion pairs of abelian categories. (The talk is based on joint works with Emanuel Diaconescu and Mauro Porta.)

3. Departmental Seminar

   From Hilbert schemes of points on a smooth surface to cohomological Hall algebras

   ICMAT, Madrid, Spain, Jul 2023

   PDF
4. Research Visit

   ICMAT, Madrid, Spain, Jul 2023

   5-week visit
5. Departmental Seminar

   From Hilbert schemes of points on a smooth surface to cohomological Hall algebras

   SISSA, Trieste, Italy, May 2023

   PDF
6. Research Visit

   SISSA, Trieste, Italy, May 2023

   3-week visit
7. Departmental Seminar

   From Hilbert schemes of points on a smooth surface to cohomological Hall algebras

   Università degli Studi di Milano, Italy, May 2023

   PDF
8. Conference Talk

   Cohomological Hall algebras and affine Yangians

   Gauge Theory, Moduli Spaces and Representation Theory, Kashiwa 2023. In honor of the 60th birthday of Hiraku Nakajima. Kavli IPMU, Tokyo, Japan, Mar 2023

   Abs WEBSITE

   After a brief introduction to the theory of (2-dimensional) cohomological Hall algebras (COHAs) of quivers, curves, and surfaces, I will discuss the COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S set-theoretically supported on a closed subscheme Z. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) via the Yangian of the corresponding affine ADE quiver. (joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.)

9. Research Visit

   Kavli IPMU, the University of Tokyo, Japan, Mar 2023

   5-week visit
10. Conference Talk

    Yangians and Cohomological Hall Algebras of Curves

    A conference on moduli spaces and vertex algebras. The University of Auckland, New Zealand, Feb 2023

    Abs WEBSITE PDF

    The talk aims to provide a gentle overview of the theory of 2-dimensional cohomological Hall algebras (COHAs) and its relation to the theory of moduli stacks and spaces, and of vertex algebras. Particular attention will be given to the COHAs associated to the moduli stacks arising from the non-abelian Hodge correspondence, i.e., the moduli stack of Higgs sheaves on a smooth projective complex curve X and the character stack of X. If time permits, the case of the cohomological Hall algebra of the Higgs sheaves on the projective line will be discussed in detail, in particular, its description in terms of affine Yangians.

11. Departmental Seminar

    Yangians from a geometric perspective

    Università degli Studi di Modena e Reggio Emilia, Italy, Feb 2023

2022

1. Departmental Seminar

   Cohomological Hall algebras, moduli spaces, and quantum groups

   Jagiellonian University, Poland, Dec 2022

   PDF
2. Departmental Seminar

   Cohomological Hall algebras, moduli spaces, and quantum groups

   Universidad Nacional de Colombia, Colombia, Nov 2022

   PDF
3. Departmental Seminar

   Cohomological Hall algebras, moduli spaces, and quantum groups

   Università di Roma La Sapienza, Italy, Oct 2022
4. Conference Talk

   Cohomological Hall algebras and affine Yangians

   Enumerative Invariants, Quantum Fields and String Theory Correspondences. Mittag-Leffler Institute, Sweden, Jul 2022

   Abs WEBSITE

   The first part of the talk is devoted to a gentle overview of the theory of 2-dimensional cohomological Hall algebras of quivers, their relations to Maulik-Okounkov Yangians, and vertex algebras (in the case of the one-loop quiver, the latter is motivated by the Alday-Gaiotto-Tachikawa conjecture for the complex plane). The second part of the talk will focus on cohomological Hall algebras of surfaces. In details, I will discuss the case when the surface is a minimal resolution of an ADE singularity. If time permits, I will speculate about possible relations to vertex algebras, motived by the Alday-Gaiotto-Tachikawa conjecture for ADE singularities.

5. Research Visit

   Université de Strasbourg, France, Jun 2022

   2-week visit
6. Departmental Seminar

   Cohomological Hall algebras, moduli spaces, and quantum groups

   Università di Bologna, Italy, Jun 2022
7. Conference Talk

   Representations of cohomological Hall algebras of surfaces via stable pairs

   Interactions between Algebraic Geometry and Noncommutative Algebra. MFO, Oberwolfach, Germany, May 2022
8. Departmental Seminar

   Two-dimensional cohomological Hall algebras

   Virginia Commonwealth University, USA, Feb 2022

   Abs PDF

   The present talk aims at introducing the theory of 2-dimensional cohomological Hall algebras and their relations with moduli spaces in algebraic geometry and representation theory. In the second part of the talk, I will focus on those associated to curves and surfaces and discuss their categorification. If time permits, I will describe in detail the cohomological Hall algebra of a Kleinian surface singularity.