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NCTS Course: Frobenius Manifolds For Everbody
 
March 31 03:40-05:50 pm , April 1 11:00-03:00 pm , March 31 - April 1, 2017
Room 440, Astronomy-Mathematics Building, NTU

Speaker:
Martin Guest (Waseda University)


Organizers:
Nan-Kuo Ho (National Tsing Hua University)
Mao-Pei Tsui (National Taiwan University)


March 31
03:40-04:40 pm  Talk 1
04:40-04:50pm   Break 
04:50-05:50pm   Talk 2 
 
April 1  
11:00-12:30pm   Talk 3
12:30-01:30pm   Lunch break 
01:30-03:00pm   Talk 4

 

Abstract

It is 20 years since the publication of "Geometry of 2D topological field theories" in volume 1620 of Lecture Notes in Mathematics by Boris Dubrovin.  In this tour de force of ideas and examples, the theory of Frobenius manifolds was firmly established. 

Frobenius manifolds are differential geometric objects, motivated by deformations of quantum field theories, unfoldings of singularities, and quantum cohomology.  Dubrovin's definition introduced a common framework for these rather different subjects.  Then he applied tools from the theory of integrable systems to obtain deep and surprising relations between them.  

In these lectures we shall try to explain what Dubrovin did, focusing on the case of 2-dimensional Frobenius manifolds where everything can be calculated explicitly by elementary methods. For Lectures 1 and 2, knowledge of 2nd order linear o.d.e. and linear algebra will be sufficient. Ideally, the listener will not notice the gradual submersion into a difficult subject (mirror symmetry).  In particular, prior knowledge of physics or algebraic geometry will not be assumed. In Lecture 3 we shall mention more advanced topics and reflect on what the theory of Frobenius manifolds has achieved.



Contact: Loreina Hsien,loreinahsien@ncts.ntu.edu.tw, 02-3366-8814



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