Department of

# Mathematics

Seminar Calendar
for events the day of Monday, December 7, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    November 2015          December 2015           January 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30
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Monday, December 7, 2015

4:00 pm in 145 Altgeld Hall,Monday, December 7, 2015

#### Multilocal bosonization and fermionization

###### Iana Anguelova (College of Charleston)

Abstract: Bosonization, namely the representation of given chiral fields (Fermi or Bose) via bosonic fields, has long been studied both in the physics and the mathematics literature, especially in connection to representation theory and integrable systems. Perhaps the best known instance is the bosonization of the charged free fermions: one of the two directions of a chiral isomorphism often referred to as "the" boson-fermion correspondence (of type A). The opposite process, fermionization, refers to the representation of given fields in terms of fermionic fields, as in the case of the representation of the Heisenberg bosonic current as a normal ordered product of the charged fermions. In this talk we discuss new instances of bosonization and fermionization, obtained by allowing multi-locality, i.e., poles in operator product expansions at roots of unity. One such new instance is the multilocal bosonization of the $\beta\gamma$ boson ghost system, and generally of the symplectic bosons (and consequently certain classes of lattice vertex algebras, of type C). Another example is the multilocal fermionization of the charged free fermions by neutral fermions, which in turn allows us to bosonize the neutral fermions, thereby completing the boson-fermion correspondence of type D.

#### The pricing of contingent claims and optimal positions in asymptotically complete markets

###### Dr. Konstantinos Spiliopoulos (Boston University )

Abstract: We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated Gartner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black-Scholes-Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models. This is joint work with Scott Robertson and Michalis Anthropelos.

4:00 pm in 141 Altgeld Hall,Monday, December 7, 2015

#### To be announced

###### Hamed Khalilian

4:00 pm in 245 Altgeld Hall,Monday, December 7, 2015

#### No meeting today

5:00 pm in 241 Altgeld Hall,Monday, December 7, 2015