Department of

February 2018March 2018April 2018 Su Mo Tu We Th Fr Sa Su Mo TuWeTh Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 1 2 3 1 2 3 4 5 6 7 4 5 6 7 8 9 10 4 5 6 7 8 9 10 8 9 10 11 12 13 14 11 12 13 14 15 16 17 11 12 13 14 15 16 17 15 16 17 18 19 20 21 18 19 20 21 22 23 24 18 19 202122 23 24 22 23 24 25 26 27 28 25 26 27 28 25 26 27 28 29 30 31 29 30

Tuesday, January 16, 2018

**Abstract:** For a compact Riemann surface of genus $g\ge 2$, the components of the moduli space of $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Higgs bundles, or equivalently the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$ character varieties, are partially labeled by an integer $d$ known as the Toledo invariant. The subspace for which this integer attains a maximum has been shown to have $3\cdot {{2}^{2g}}+2g-4$ many components. A gluing construction between parabolic Higgs bundles over a connected sum of Riemann surfaces provides model Higgs bundles in a subfamily of particular significance. This construction is formulated in terms of solutions to the Hitchin equations, using the linearization of a relevant elliptic operator.

Tuesday, January 23, 2018

Tuesday, January 30, 2018

Monday, February 5, 2018

Thursday, February 15, 2018

Tuesday, February 20, 2018

Tuesday, March 6, 2018

Tuesday, March 13, 2018

Tuesday, March 27, 2018

Tuesday, April 10, 2018

Tuesday, April 24, 2018