In August I submitted my DPhil Thesis at the University of Oxford, under the supervision of Nigel Hitchin , where I looked at Higgs bundles for real forms by defining spectral data associated to them and studying these new objects. In particular, our construction gives directly the desingularization of the necessarily singular spectral curves associated to orthogonal Higgs bundles. The growth of snow crystals is dependent on the temperature and saturation of the environment. During the second lecture we construct Higgs bundles for real forms of classical complex Lie groups as fixed points of involutions, and describe the corresponding spectral data when known. Surface groups in Paris. Alison Etheridge with undergraduate mathematics entrance interviews. I am a member of Prof.
Remember me on this computer. Exchange program Grant, National Science Foundation. Higgs bundles and A,B,A -branes , with D. Workshop on the moduli space of Higgs bundles. My first approach to principal Higgs bundles was when looking at the monodromy action for SL 2,R Higgs bundles. New College, Oxford, UK.
Spectral data for principal Higgs Bundles. Spectral data for G-Higgs xchaposnik. 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.
Spectral data for G-Higgs bundles Graduate ScholarNew College, Oxford. 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: Twistors, Geometry and Physics.
In the case of dendrites, Reiter’s local two-dimensional model provides a realistic approach to the study of dendrite growth. Skip to main content.
International Journal of Mathematics, Vol. September Mar del Plata, Argentina. During the last years I have been studying the moduli space of principal Higgs bundles and its relation to other areas of mathematics and physics. II Latinoamerican conference on Lie groups in geometry.
Spectral data for U m,m -Higgs bundles Short visit Grant, National Science Foundation. January and June August La Cumbre, Cordoba, Argentina. National Government Prize Awards to the best undergraduate student of the year. 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.
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.
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Here is my Project 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.
My first approach to principal Higgs bundles was when looking at the monodromy action for SL 2,R Higgs bundles. Click here to sign up. PDF file in Spanish. National University of La Plata. Algebraic Number Theory, Class Tutor: Victor Flynn Graduate advisor and teaching reference.
View of Oxford from the tower of New College. Summer School on the moduli space of Higgs bundles. Higgs bundles and A,B,A -braneswith D. Mathematics and Physics of moduli spaces, Heidelberg, Germany. View of Oxford from the tower of New College.
In this work we constructed natural A,B,A -branes associated to anti-holomorphic involutions on compact Riemann surfaces. We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory. The first lecture introduces classical Higgs bundles and the Hitchin fibration, and describe the associated spectral data in the case of lajra Higgs bundles for classical complex Lie groups.
Schaopsnik the second lecture we construct Higgs bundles for real forms of classical complex Lie groups as fixed points of involutions, and describe the corresponding spectral data when known.