Johannes Walcher
Mathematical Physics, Heidelberg University
Office: Im Neuenheimer Feld 205, Room 5/204
Contact: walcher@uni-heidelberg.de

## Welcome

We are bridging the stream between theoretical high-energy physics, and algebraic and analytic sub-disciplines of geometry. We are interested in the mathematical theories that are relevant for the fundamental description of nature, and use physical intuition to uncover new structures. On a first visit, take a look at the current seminar schedule.

## News

• No Office hour until December 21st. Please send me an Email.
• Teaching in the Winter 18/19: Dr. Saberi's lecture is here.
• Die Zweitklausur zur Höheren Mathematik II findet statt am Montag, dem 8. Oktober 2018, von 17h00 bis 19h00, im INF 227 / HS1.
• 07/10/18: New paper! — The nilpotence variety of a super Lie algebra is the geometric locus of odd elements that square to zero. Inside of super Poincaré algebras, such elements define topological and holomorphic twists of supersymmetric quantum field theories, which are unified by the geometric perspective. Homological algebra provides a bridge to the pure-spinor superfield formalism, which we will overcome in upcoming work. Some of our examples are new, inlcuding: a calculation of Chevalley-Eilenberg cohomology for the six-dimensional ${\mathcal N}=(2,0)$ supertranslation algebra, and a BV complex matching the field content of type IIB supergravity from the coordinate ring of the corresponding nilpotence variety. (With Richard Eager and Ingmar Saberi)
• Teaching in the Summer 18: The lecture is here, the seminar here.
• 02/21/18: Still looking for tutors for Mathematics for Physicists II (Summer 18). Interested candidates please contact me ASAP!
• Office hour in the Winter term: Wednesday, 11am-noon and by appointment
• Teaching in the Winter 16/17: The lecture is here.
• 06/14/17: Office hour is cancelled.
• Office hour in the Summer term: Wednesday, 1-2pm and by appointment
• 04/07/17: Forget Earth Day. Heidelberg University supports the March for Science Heidelberg on April 22.
• From July 20 to 22, we will host a three-day workshop on Flat connections in Physics and Geometry, supported by the Partnership Mathematics and Physics. All interested are cordially invited.
• Teaching in the Summer 17: The seminar is here, the lecture here.
• 02/23/17: New paper! — Obsessions of topological string theorists include rigidity, integrality, and modularity. In the B-model, the enumerative interpretation of topological amplitudes remains poorly understood (but see exponential networks), so integrality is best established by appealing to arithmetic properties of the background geometry. This is a fortiori true when the amplitudes turn out to be irrational. Generalizing the method developed by Kontsevich, Schwarz and Vologodsky, we establish this integrality of the superpotential for D-branes wrapping algebraic cycles. Along the way, we give a general proof that the so-called framing transformation preserves integrality of topological string amplitudes. (With Albert Schwarz and Vadim Vologodsky)
• Die Zweitklausur zur Höheren Mathematik III findet statt am Samstag, dem 22. April 2017, 9-11, INF 227 / HS1. Donnerstag, dem 20. April 2017, 14-16h, INF 308 / HS1.
• Office hour in the Spring break: by appointment.
• 01/31/17: We are looking for a teaching assistant/grader for the course "Differential geometry 1" (Elective in Mathematics Bachelor programm). Interested candidates with the appropriate background please contact me by Email. Update 02/24/17: The team is complete.
• 12/07/16: Office hour moved to 12pm.
• 11/02/16: Office hour is cancelled.
• Office hour in the Winter term: Wednesday, 1-2pm
• 11/18/16: New paper! — Spectral networks were introduced some time ago by Gaiotto, Moore and Neitzke for the parametrization of BPS spectra in certain classes of gauge theories with extended supersymmetry. In particular, such networks provide a concrete realization of the very general Kontsevich-Soibelmann wall-crossing formula (KSWCF). Spectral networks have also proven very useful for the parametrization of moduli spaces of flat connections on Riemann surfaces in the study of Hitchin systems. With Richard and Sam, we initiate the lifting of spectral networks to local Calabi-Yau geometries. The main new features are logarithmic cuts in the differential and a subtle junction rule for trajectories with multiplicity. Our initial goal was to reproduce known spectra of toric Calabi-Yaus via the representation theory of their associated BPS quivers. A proof of the KSWCF is forthcoming, and applications to (group valued?) Hitchin systems around the corner.
• Die Zweitklausur zur Höheren Mathematik II findet statt am Montag, dem 10. Oktober 2016, von 17h00 bis 19h00, im INF 227 / HS1.
• Vorbesprechung zum Proseminar Mechanik: Am Mittwoch, 12.10., 15-17h, Raum 0/200 MATHEMATIKON
• Teaching in the Winter 16/17: The seminar is here, the lecture here. Exam specifics.
• 08/04/16: Still looking for tutors for Mathematics for Physicists III (Winter 16/17). Interested candidates please contact me ASAP.
• In August, Ron Donagi and Tony Pantev will give a series of lectures on Hitchin fibrations and the geometric Langlands correspondence in Heidelberg.
• 03/15/16: We are moving to the Mathematikon!
• Teaching in the Summer 16: The seminar is here, the lecture here. Exam specifics.
• 02/01/16: Still looking for tutors for Mathematics for Physicists II (Summer 16). Interested candidates please contact me ASAP. Not anymore!
• Teaching in the Winter 15/16: The seminar is here, the lecture here.
• 09/23/15: A 2+1yrs postdoctoral position at the interface of physics and geometry is available to begin in Fall 2016. The "official" job posting can be found here, applications are now being accepted via MathJobs.Org.
• 08/20/15: We are looking for a teaching assistant/grader for the course "Lie groups and representation theory" (Elective in Bachelor Math/Physics). Interested candidates with the appropriate background please contact me by Email.
• Coming soon: Information about teaching in Winter 2015/16
• Event this Summer: Workshop Hidden symmetries and integrability methods in super Yang-Mills theories and their dual string theories, CRM Montreal — Part of Thematic Semester AdS/CFT, Holography, Integrabiliy