The seminar Interactions between symplectic geometry, combinatorics and number theory will cover different topics, and is aimed at studying the interactions among them. In particular, we will learn about genera on complex or symplectic manifolds (for instance the Todd and Hirzebruch genus and elliptic genera) and their connections with modular forms, as well as the combinatorics of lattice polytopes, in particular Ehrhart theory and reflexive polytopes.

 

Graduate students, postdocs and professors interested in attending will be encouraged to give explanatory talks that are suitable to an audience with diverse background.

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From time to time we will also invite external speakers to give more advanced/research talks on topics related to those covered in this seminar.

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16.10.17: Milena Pabiniak, "The decomposition of a polytope into its cones"

23.10.17: Isabelle Charton, "The decomposition of a polytope into its cones, Part II"

30.10.17: Silvia Sabatini, "Combinatorial K-theory: Definition of Index"

06.11.17: Silvia Sabatini, "Convexity properties of the Index and multiplicities"

13.11.17: Alexander Caviedes Castro, "Euler–Maclaurin Summation in R^d" 

20.11.17: Christian Steinert, "An introduction to toric degenerations"

27.11.17: Lara Bossinger, "Examples of toric degenerations"

04.12.17: Hendrik Suess (U. Manchester), "T-equivariant toric degenerations and connections to symplectic geometry"

11.12.17: No seminar

18.12.17: Benjamin Nill (U. Magdeburg), "On the geometry of numbers of lattice polytopes"

08.01.18: Alexander Caviedes Castro, "Irreducible representations and Weyl character formula"

15.01.18: Thomas Eckl (U. Liverpool), "Local Positivity in Algebraic Geometry and Symplectic Topology"

22.01.18: Nikhil Savale, "Bergman Kernel on toric Kähler manifolds"

29.01.18: Mohammad Bardestani, "On the chromatic number of structured Cayley graphs"

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Bibliography:

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- "Computing the continuous discretely" by M. Beck and S. Robins

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- "G-actions on graphs", by V. Guillemin and C. Zara, Int. Math. Res. Notices 2001, no. 10, 519--542

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