19 FEB 2025
17:30 - 19:00

We discuss construction of a derived Lagrangian intersection theory of moduli spaces of perfect complexes, with support on divisors on compact Calabi Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We apply a Tyurin degeneration of the CY3 into a normal-crossing singular variety composed of Fano threefolds meeting along their anti-canonical divisor. We show that the moduli space over the Fano 4 fold given by total space of degeneration family satisfies a relative Lagrangian foliation structure which leads to realizing the moduli space as derived critical locus of a global (-1)-shifted potential function. We construct a flat Gauss-Manin connection to relate the periodic cyclic homology induced by matrix factorization category of such function to the derived Lagrangian intersection of the corresponding ?Fano moduli spaces?. The later provides one with categorification of DT invariants over the special fiber (of degenerating family). The alternating sum of dimensions of the categorical DT invariants of the special fiber induces numerical DT invariants. If there is time, we show how in terms of ?non-derived? virtual intersection theory, these numerical DT invariants relate to counts of D4-D2-D0 branes which are expected to have modularity property by the S-duality conjecture. This talk is based on joint work with Ludmil Katzarkov and Maxim Kontsevich, recent work with Jacob Krykzca, and former work with Vladimir Baranovsky.

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Meeting ID: 9086116889
Passcode: 362880
Website: http://math.ipm.ac.ir/agnt/
Venue: Niavaran, Lecture Hall 1

19 FEB 2025
15:30 - 17:00

The pants graph of a compact orientable surface S, introduced by Hatcher and Thurston, is a simplicial graph whose vertices are maximal essential multicurves on S and whose edges correspond to certain local moves on multicurves. The importance of the pants graph comes from a theorem of Brock showing that the pants graph is a good combinatorial model for the Teichmuller space with the Wiel-Petersson metric, which is the space of hyperbolic metrics on S up to isotopy. In joint work with Marc Lackenby, we give upper bounds for distance in the pants graph and derive applications for distance in the Teichmuller space and also for volumes of hyperbolic 3-manifolds. I will give an overview of these results, no prior familiarity with the Teichmuller is needed for the talk.

Online via Zoom:
Meeting ID: 908 611 6889
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

19 FEB 2025
14:00 - 15:00

Many combinatorial optimization problems have been studied in the prize collecting setting, where the coverage requirement for an entity can be relaxed by paying a predefined penalty. This resembles the classical Lagrangian relaxation, and is natural in many practical applications. In this talk we discuss approximation algorithms for the prize-collecting version of the Traveling Salesman Problem (TSP) and some of its generalizations.

Zoom room information:
https://us06web.zoom.us/j/84906984159?pwd=BCWaIbXBuku3A5I84zNg9mHFxVZjXD.1
Meeting ID: 849 0698 4159
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

12 FEB 2025
15:30 - 17:30

This lecture is a continuation of the lecture of about a year ago with the same title. No familiarity with the last lecture will be assumed and the emphasis will be on topics that were not discussed in the previous lecture and have some novelty.
Venue: Niavaran, Lecture Hall 1

6 FEB 2025
14:00 - 16:00



Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

5 FEB 2025
15:30 - 17:00

Kahler manifolds appear naturally in both Algebraic and Differential Geometry: projective complex varieties from Algebraic Geometry, and smooth manifolds with Riemannian metrics with holonomy U(n). Understanding when a manifold may admit a Kahler structure and how far it is from that is a key problem in geometry. Classically, tools from global analysis (harmonic forms and Hodge theory) provide striking topological properties of Kahler manifolds, linking topology and analysis. We shall review this circle of ideas, and recent results on the construction of manifolds admitting complex structures (and even both complex and symplectic structures simultaneously) but not admitting Kahler structures.

Venue: Online via Zoom:
Meeting ID: 894 4268 0102
Passcode: 362880
Venue: , (Online)

5 FEB 2025
18:00 - 19:00

Join Zoom Meeting:

https://zoom.us/j/96203909682?pwd=TlKeYkJ2lVW4cGKkGnvLPL0PEsd2of.1


Meeting ID: 962 0390 9682

Passcode: 716850

29 JAN 2025
15:30 - 17:00

Actions of algebraic groups appear in many problems of Algebraic Geometry, encoding certain symmetries. Often one is interested in factoring out these symmetries and producing a new geometric object, a so-called quotient that parametrises the orbits of the action. In this framework, Geometric Invariant Theory (GIT) developed by David Mumford in 1965 deals with the problem of the existence of quotients, with an algebro-geometric structure, of an algebraic variety by the action of a reductive group. This method is extremely useful which also has important and surprising connections with symplectic geometry. In this lecture we shall give a gentle introduction to GIT construction, mainly focusing on the affine case. The algebraic side of this story is about finding the subalgebra of invariants (for an algebra with a group action) which dates back to Hilbert?s 14th problem.




Online via Zoom:


Meeting ID: 908 611 6889


Passcode: 362880
Venue: Niavaran, Lecture Hall 1