Spring 2026: (all meetings in person)
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1/30: Prof. Sisi Shen (City Tech, CUNY)
Title: The continuity equation for Hermitian metrics
Abstract: Initially introduced by La Nave-Tian, the continuity equation is an elliptic analogue to the K\"ahler-Ricci flow which serves as an alternative way of tackling the Analytic Minimal Model program. Sherman-Weinkove generalized this work to the Hermitian setting, providing an elliptic analogue to the Chern-Ricci flow. We will discuss the behavior of solutions to the continuity equation on Hopf and Inoue surfaces as well as Oeljeklaus-Toma manifolds and compare and contrast the advantages and disadvantages of this approach. In addition, we will discuss some new results on coupled continuity equations that can be used to study the cscK problem.
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2/6: Special event, time and place:
Congratualtions to Prof. Mehdi Lejmi (Bronx, CUNY) as recipient of the
Sandi Cooper Award for his mathematical research.
Mehdi and other awardees will give short talk at the award ceremony at 1pm on the 8th floor.
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2/13: Prof. Kuan-Hui Lee (McGill University)
Title: The stability of steady generalized Ricci solitons
Abstract: Non-Kähler Calabi-Yau theory is a newly developed subject, and it arises naturally in mathematical physics and generalized geometry. The relevant geometries are pluriclosed metrics which are critical points of the generalized Einstein–Hilbert action which is an extension of Perelman’s F-functional. In this talk, we studied the non-Kähler Calabi-Yau through pluriclosed flow which was first introduced by Streets and Tian a few years ago. We study the critical points of the generalized Einstein-Hilbert action and discuss the stability of critical points which are defined as pluriclosed steady solitons. We proved that all compact Bismut–Hermitian–Einstein metrics are linearly stable.
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2/20: TBA
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2/27: Prof. Manuel Rivera (Purdue U.)
Title: String topology via the coHochschild complex
Abstract: I will describe a tractable chain-level model for the free loop space of a simplicial complex. The construction is based on coHochschild homology theory for coalgebras and does not assume any restrictions on the fundamental group or the commutative ring of coefficients.
I will then describe a way of lifting Poincaré duality to the chain level by adapting the formalism of Pre-Calabi Yau structures (developed independently by Tradler/Zeinalian and Kontsevich/Takeda/Vlassopoulos) to our setting.
Combining the two ingredientes above we produce algebraic formulae for string topology of (possibly non-simply connected) homology manifolds. From these formulae one can observe that assuming locality conditions on the chain-level lift of Poincare duality are necessary to recover the loop coproduct, an operation that can distinguish homotopy equivalent non-homeomorphic manifolds. This is joint work with Alex Takeda.
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3/6: Prof. David Pham (CUNY)
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3/13: Prof. Junsheng Zhang (NYU)
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3/20: no classes at CUNY (no meeting)
3/27: Prof. Bin Guo (Rutgers)
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4/3: no meeting (Spring break)
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4/10: no meeeting
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4/17: Prof. Ralph Gomez (Swarthmore College)
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4/24: Prof. Christoforos Neofytidis (University of Cyprus)
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5/1: Prof. Max Hallgren (Rutgers)
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5/8: TBA
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5/15: TBA
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