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- Non-abelian Hodge theory in dimension one, Fukaya categories and periodic monopoles.

By the non-abelian Hodge theory of Carlos Simpson, harmonic bundles

interpolate between bundles with connections on a curve and

Higgs bundes (precise formulations requires some additional data like parabolic structure and stability structure).

I will explain the framework for a generalization of the non-abelian Hodge theory

which unifies Simpson's story ("rational case") with those for q-difference

equations ("trigonometric case") and elliptic difference equations

("elliptic case").

This unification leads to a class of examples of the new notion of ``twistor families of categories".

In the rational,trigonometric and elliptic cases twistor families of categories involve partially wrapped Fukaya categories of certain complex symplectic surfaces, categories of

holonomic modules over quantizations of these surfaces and categories of coherent sheaves on the surfaces

with certain restrictions on the support.

In the trigonometric and elliptic cases doubly and triply periodic monopoles give an alternative description of harmonic objects, hence playing the same role

as harmonic bundles play in the case of Simpson theory.

Collection/Series:

Event Type:

Seminar

Scientific Area(s):

Speaker(s):

Event Date:

Monday, January 8, 2018 - 14:00 to 15:30

Location:

Sky Room

Room #:

394

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