Enumerative Geometry and Geometric Representation Theory

Jun 23, 2025, 9:30 AM → Jul 4, 2025, 5:30 PM Europe/Rome

Università di Pisa, Italy

The Summer School on "Enumerative Geometry and Geometric Representation Theory" will take place at the Centro Congressi Le Benedettine, in Pisa, from June 23 to June 29 and at the Aula G, Polo Fibonacci, of the University of Pisa, from June 30 to July 4, 2025. It can be seen as a second iteration of the 2021 IHÉS Summer School on "Enumerative Geometry, Physics and Representation Theory" organized by Neguţ, Sala, and Schiffmann. 

The school offers six 5-hour lectures together with exercise/Q&A sessions and Advanced Research sessions. 

The school welcomes everybody but is primarily intended for Ph.D. students and young postdocs.

The Summer School focuses on the following main subjects: 

• logarithmic and tropical geometry and relations to enumerative geometry
• the geometry of the Hitchin moduli space
• Donaldson-Thomas invariants, BPS states, and their categorification
• Cohomological Hall algebras and their relation to enumerative geometry
• Coulomb branches in geometry and representation theory

You can find the recordings of the lectures on the Department’s YouTube channel: link.

 

We have limited funds. We may ONLY offer accommodations in shared rooms to a limited number of participants. If you need support, please let us know through the registration procedure.
Deadline for requesting support: February 15, 2025.

 

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Lecturers

Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Joel Kamnitzer (McGill University, Montreal, Canada)

Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

Junliang Shen (Yale University, USA)

Bernd Siebert (The University of Texas at Austin, USA)

Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)     

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Advisors for the Afternoon Sessions

Hülya Argüz (University of Georgia, USA)

Camilla Felisetti (Università di Modena e Reggio Emilia)

Lucien Hennecart (CNRS and Université de Picardie Jules Verne, France)

Samuel Johnston (Imperial College London, UK)

Dinakar Muthiah (University of Glasgow, UK)

Tudor Pădurariu (CNRS and Sorbonne Université, France)

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Gong Show

Danil Gubarevich (Université de Paris-Saclay, France)

Mischa Elkner (IST, Austria)

Shivang Jindal (University of Edinburgh, UK)

Jingxiang Ma (University of Sheffield, UK)

Timm Peerenboom (Ruhr-Universität Bochum, Germany)

Jeremy Peters (University of Toronto, Canada)

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Poster Session

Rostislav Devyatov (Higher School of Economics, Moscow, Russia): Multiplicity-free products of Schubert divisors

Sabino Di Trani (Sapienza Università di Roma, Italy): TBA

Noah Dizep (Heriot Watt University, UK): Quantum Periods for Calabi-Yau Threefolds

David Fang (Yale University, USA): Fourier-Mukai transforms of certain upward flows in moduli spaces of Higgs bundles

Luca Francone (Università di Roma Tor Vergata, Italy): Cluster structures on schemes of bands

Zelin Jia (Nagoya University, Japan): Symplectic geometry of Higgs moduli and the Hilbert scheme of points over an elliptic curve

Nhok Tkhai Shon Ngo (IST, Austria): Hausel's big algebras in type A and Bethe subalgebras of the Yangian Y(gl_n)

Parth Shimpi (University of Glasgow, UK): What's on my rational curve?

Fei Si (Xi’an Jiaotong University, China): TBA

Xinyue Tu (The Chinese University of Hong Kong, China): Quantum cohomology and intersection cohomology-divisorial case

Keke Zhang (Perimeter Institute, Canada): The Quantum Hikita Conjecture

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Scientific Committee

Andrei Neguţ (EPFL, Switzerland)

Francesco Sala (Università di Pisa)

Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

Mattia Talpo (Università di Pisa)

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Organizing Committee

Pietro Leonardini (Università di Pisa)

Andrea Maffei (Università di Pisa)

Francesco Sala (Università di Pisa)  

Mattia Talpo (Università di Pisa)

Bernando Tarini (Scuola Normale Superiore, Pisa)

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The Summer School is supported by the Department of Mathematics, University of Pisa (Dipartimento di Eccellenza -- CUP I57G22000700001), Prin 2022 "Algebraic and geometric aspects of Lie theory" (2022S8SSW2), Prin 2022 "Geometry of algebraic structures: moduli, invariants, deformations" (2022BTA242), and by Scuola Normale Superiore.
 

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During the School, violence, harassment, or discrimination of any sort are not tolerated. In case you witness or are subject to such behaviors, contact the competent authorities. For further information, please ask the organizers.

poster.pdf

Monday, June 23

9:30 AM Registration

9:55 AM Welcome

1 Donaldson--Thomas Theory, Flow Trees and Log Gromov--Witten Invariants

Speaker: Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Bousseau_pisa_lectures_1_2.pdf

11:00 AM Coffee Break

2 Donaldson--Thomas Theory, Flow Trees and Log Gromov--Witten Invariants

Speaker: Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Bousseau_pisa_lectures_1_2.pdf

12:30 PM Lunch break

3 Logarithmic Gromov-Witten invariants and its application to mirror symmetry

Speaker: Bernd Siebert (The University of Texas at Austin, USA)

I. Introduction to Log Geometry.pdf

4:00 PM Break

4 From quantum cohomology of symplectic resolutions to compactifications of families of Gaudin algebras

Speaker: Joel Kamnitzer (McGill University, Montreal, Canada)

Quantum cohomology of symplectic resolutions and moduli spaces of Gaudin algebras.pdf

Tuesday, June 24

5 From quantum cohomology of symplectic resolutions to compactifications of families of Gaudin algebras

Speaker: Joel Kamnitzer (McGill University, Montreal, Canada)

Quantum cohomology of symplectic resolutions and moduli spaces of Gaudin algebras.pdf

11:00 AM Coffee Break

6 Logarithmic Gromov-Witten invariants and its application to mirror symmetry

Speaker: Bernd Siebert (The University of Texas at Austin, USA)

II. Tropicalization and Log Smooth Curves.pdf

12:30 PM Lunch Break

7 Donaldson--Thomas Theory, Flow Trees and Log Gromov--Witten Invariants

Speaker: Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Bousseau_pisa_lecture3.pdf

4:00 PM Break

8 Exercise Session: Calculating quiver DT/log Gromov-Witten invariants in higher dimensions

Speaker: Hülya Argüz (University of Georgia, USA)

9 Exercise Session: The BFN construction of Coulomb branches, symplectic duality, and affine Grassmannians slices

Speaker: Dinakar Muthiah (University of Glasgow, UK)

10 Exercise Session: The tropical geometry of the moduli space of log smooth curves

Speaker: Samuel Johnston (Imperial College London, UK)

Wednesday, June 25

11 From quantum cohomology of symplectic resolutions to compactifications of families of Gaudin algebras

Speaker: Joel Kamnitzer (McGill University, Montreal, Canada)

Lecture3.pdf

11:00 AM Coffee Break

12 Logarithmic Gromov-Witten invariants and its application to mirror symmetry

Speaker: Bernd Siebert (The University of Texas at Austin, USA)

III. Logarithmic Gromov-Witten Invariants, Artin Fans.pdf

12:30 PM Break

13 Gong Show: Wheel conditions for reductive groups

Speaker: Danil Gubarevich (Université de Paris-Saclay, France)

14 Gong Show: Mirror symmetry for ADE resolutions

Speaker: Jingxiang Ma (University of Sheffield, UK)

15 Gong Show: Parameter spaces for quantum cohomology

Speaker: Jeremy Peters (University of Toronto, Canada)

1:25 PM Free Afternoon

Thursday, June 26

16 Donaldson--Thomas Theory, Flow Trees and Log Gromov--Witten Invariants

Speaker: Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Bousseau_pisa_lecture4.pdf

11:00 AM Coffee Break

17 Logarithmic Gromov-Witten invariants and its application to mirror symmetry

Speaker: Bernd Siebert (The University of Texas at Austin, USA)

IV. Punctured Gromov-Witten Invariants and the Gluing Formalism.pdf

12:30 PM Lunch Break

2:15 PM Poster Session

18 From quantum cohomology of symplectic resolutions to compactifications of families of Gaudin algebras

Speaker: Joel Kamnitzer (McGill University, Montreal, Canada)

Lecture4.pdf

4:00 PM Break

19 Exercise Session: Calculating quiver DT/log Gromov-Witten invariants in higher dimensions

Speaker: Hülya Argüz (University of Georgia, USA)

20 Exercise Session: The BFN construction of Coulomb branches, symplectic duality, and affine Grassmannians slices

Speaker: Dinakar Muthiah (University of Glasgow, UK)

21 Exercise Session: The tropical geometry of the moduli space of stable log maps

Speaker: Samuel Johnston (Imperial College London, UK)

Friday, June 27

22 Logarithmic Gromov-Witten invariants and its application to mirror symmetry

Speaker: Bernd Siebert (The University of Texas at Austin, USA)

V. Intrinsic Mirror Symmetry.pdf

11:00 AM Coffee Break

23 Donaldson--Thomas Theory, Flow Trees and Log Gromov--Witten Invariants

Speaker: Pierrick Bousseau (University of Georgia, USA, and CNRS, France)

Bousseau_pisa_lecture5.pdf

12:30 PM Lunch Break

24 From quantum cohomology of symplectic resolutions to compactifications of families of Gaudin algebras

Speaker: Joel Kamnitzer (McGill University, Montreal, Canada)

Lecture5.pdf

4:00 PM Break

25 Research Session: Kac-Moody affine Grassmannian slices

Speaker: Dinakar Muthiah (University of Glasgow, UK)

26 Research Session: Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs

Speaker: Hülya Argüz (University of Georgia, USA)

27 Research Session: Quantum periods, toric degenerations and intrinsic mirror symmetry

Speaker: Samuel Johnston (Imperial College London, UK)

Monday, June 30

28 Decomposition Theorem for abelian fibrations

Speaker: Junliang Shen (Yale University, USA)

11:00 AM Coffee Break

29 Decomposition Theorem for abelian fibrations

Speaker: Junliang Shen (Yale University, USA)

12:30 PM Lunch Break

30 Categorical Donaldson-Thomas theory and the Dolbeault geometric Langlands conjecture

Speaker: Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)

4:00 PM Coffee Break

31 Categorical Donaldson-Thomas theory and the Dolbeault geometric Langlands conjecture

Speaker: Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)

Tuesday, July 1

32 Cohomological Hall algebras of sheaves on surfaces and applications

Speaker: Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

11:00 AM Coffee Break

33 Cohomological Hall algebras of sheaves on surfaces and applications

Speaker: Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

12:30 PM Lunch Break

34 Decomposition Theorem for abelian fibrations

Speaker: Junliang Shen (Yale University, USA)

4:00 PM Coffee Break

35 Exercise Session: Examples of cohomological Hall algebras

Speaker: Lucien Hennecart (University of Edinburgh, UK)

36 Exercise Session: Intersection cohomology and decomposition theorem, examples and exercises.

Speaker: Camilla Felisetti (Università di Modena e Reggio Emilia)

37 Exercise Session: Vanishing cycles and cohomology of stacks

Speaker: Tudor Pădurariu (CNRS and Sorbonne Université, France)

Wednesday, July 2

38 Cohomological Hall algebras of sheaves on surfaces and applications

Speaker: Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

11:00 AM Coffee Break

39 Categorical Donaldson-Thomas theory and the Dolbeault geometric Langlands conjecture

Speaker: Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)

12:30 PM Break

40 Gong Show: Quantum groups from Cohomological DT theory

Speaker: Shivang Jindal (University of Edinburgh, UK)

41 Gong Show: CoHAs of Torsion Sheaves on Weighted Projective Lines

Speaker: Timm Peerenboom (Ruhr-Universität Bochum, Germany)

42 Gong Show: Some symmetries of Hausel’s big algebras

Speaker: Mischa Elkner (IST, Austria)

1:25 PM Free Afternoon

Thursday, July 3

43 Decomposition Theorem for abelian fibrations

Speaker: Junliang Shen (Yale University, USA)

11:00 AM Coffee Break

44 Cohomological Hall algebras of sheaves on surfaces and applications

Speaker: Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

12:30 PM Lunch Break

2:15 PM Poster Session

45 Categorical Donaldson-Thomas theory and the Dolbeault geometric Langlands conjecture

Speaker: Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)

4:00 PM Coffee Break

46 Exercise Session: Semiorthogonal decompositions

Speaker: Tudor Pădurariu (CNRS and Sorbonne Université, France)

47 Exercise Session: Tools to study cohomological Hall algebras

Speaker: Lucien Hennecart (University of Edinburgh, UK)

48 Exercise Session: Weak abelian fibrations, examples and exercises.

Speaker: Camilla Felisetti (Università di Modena e Reggio Emilia)

Friday, July 4

49 Decomposition Theorem for abelian fibrations

Speaker: Junliang Shen (Yale University, USA)

11:00 AM Coffee Break

50 Cohomological Hall algebras of sheaves on surfaces and applications

Speaker: Olivier Schiffmann (CNRS and Université de Paris-Saclay, France)

12:30 PM Lunch Break

51 Categorical Donaldson-Thomas theory and the Dolbeault geometric Langlands conjecture

Speaker: Yukinobu Toda (Kavli IPMU, the University of Tokyo, Japan)

4:00 PM Coffee Break

52 Research Session: BPS Lie algebras and generalized Kac--Moody Lie algebras

Speaker: Lucien Hennecart (University of Edinburgh, UK)

53 Research Session: Decomposition theorem for abelian fibrations, examples and exercises.

Speaker: Camilla Felisetti (Università di Modena e Reggio Emilia)

54 Research Session: Semiorthogonal decompositions for categories of coherent sheaves on certain singular stacks

Speaker: Tudor Pădurariu (CNRS and Sorbonne Université, France)