Abstract
A graph can be viewed, in many respects, as a discrete analogue of an algebraic curve. We begin by formulating the theory of "divisors" on graphs and on tropical curves, and discuss the combinatorial analogues of the classical RiemannRoch theorem. We also describe the analogues of Jacobian varieties in these settings, which are intimately related to the classical matrixtree theorem. Connections with commutative algebra and algebraic geometry will also be discussed. We then turn our attention to nonarchimedean geometry (in the sense of Berkovich) and the problem of "faithful tropicalization" of abelian varieties in terms of padic and tropical theta functions.
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(The nonexpository parts will be based on joint works with M. Baker  Y. An, M. Baker, G. Kuperberg  F. Mohammadi  T. Foster, J. Rabinoff, A. Soto).
Information:
Date:  Monday and Tuesday, January 6 and 7, 2014
Time:
1st Session: Monday Jan 6, 1112:30
2nd Session: Monday Jan 6, 1415:30
3rd Session: Tuesday Jan 7, 1112:30
4th Session: Tuesday Jan 7, 1415:30
 Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
