# LAURA SCHAPOSNIK THESIS

After hearing a lot on Langlands duality and branes in the moduli space of Higgs bundles here , I started looking at what different A,B,A and B,A,A branes could be constructed in the moduli spaces of principal Higgs bundles. Here we investigate this situation, which corresponds to the coalescence of D-branes in physics terminology, including the case of Sp m,m -Higgs bundles studied in arXiv: Steven Bradlow Post-doc reference. Mathematische Arbeitstagung, Bonn, Germany. Monodromy of SL 2 -Hitchin Systems. Here is my CV.

Heidelberg Laureate Forum, Heidelberg, Germany. Nonabelianization of Higgs bundles , with N. Higgs bundles and A, B, A -branes, with D. I nterface control and snow crystal growth, with Jessica Li , The first lecture introduces classical Higgs bundles and the Hitchin fibration, and describe the associated spectral data in the case of principal Higgs bundles for classical complex Lie groups. DPhil thesis, University of Oxford

Here are my publications. In the case of certain real forms, the corresponding moduli space of Higgs bundles is closely related to the moduli space of rank 2 semistable vector bundles or parabolic bundles on an algebraic curve. These branes are closely related to representations of the surface which extend to the 3-manifold and we are currently studying this relation and its implications.

Through combinatorial methods, I could obtain an explicit description of the monodromy action on the mod 2 cohomology for SL 2,C Higgs bundles, and by understanding the orbits, obtain information about the connected components of the moduli space of real SL 2,R Higgs bundles.

Spectral data for principal Higgs Bundles. In the case of dendrites, Reiter’s local two-dimensional model provides a realistic approach to the study of dendrite growth. August La Cumbre, Cordoba, Argentina. I am a member of Prof.

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Workshop on Moduli Spaces of Representations. Twistors, Geometry and Physics. Individual tutorial, Washington University. Alison Etheridge with undergraduate mathematics entrance interviews.

July Singapore, Singapore. Spectral data for G-Higgs bundles. Heidelberg Laureate Forum, Heidelberg, Germany. Surface group representations and split real forms – When considering Higgs bundles for split real forms as sitting inside the corresponding Hitchin fibration, they are described by points of order two in the smooth fibres see arXiv: School on Moduli Spaces. During the last years I have been studying the moduli space of principal Higgs bundles and its relation to other areas of mathematics and wchaposnik.

During the last years I have been studying the moduli space of principal Higgs bundles and its relation llaura other areas of mathematics and physics. This work is based on arXiv: Monodromy of SL 2 -Hitchin Systems. International Mathematics Research Notices, We begin here a program to study exceptional isogenies between classical Lie groups at the level of Higgs bundles and representation theory.

School of Mathematics, University of Adelaide, Australia. International conference on mathematical physics. In this work we constructed natural A,B,A -branes associated to anti-holomorphic involutions on compact Riemann surfaces.

Steven Bradlow Post-doc reference. In this paper we obtain a new geometric rule that incorporates interface control, a basic mechanism of crystallization that is not taken into account oaura the original Reiter’s schappsnik. The first lecture introduces classical Higgs bundles and the Hitchin fibration, and describe the associated spectral data in the case of principal Higgs bundles for classical complex Lie groups.

Sixth workshop on Lie theory and geometry. A symplectic approach to constrained mechanical systems.

# Laura Schaposnik

Summer school on the moduli space of Higgs bundles. Monodromy of the SL2 Hitchin fibration. In August I submitted my DPhil Thesis at the University of Oxford, under the supervision of Nigel Hitchinwhere I looked at Higgs bundles for real forms by defining spectral data lauda to them and studying these new objects.

National University of La Plata. We study the real points through the associated spectral data and describe the topological invariants involved using Scbaposnik, KR and equivariant K-theory. Representations, Lie theory and physics.