Quantum Topology and Field Theory Seminar
Yale University
Fall 2025
Yale University
Fall 2025
Organizers: Andrew Neitzke, Surya Raghavendran, Charlie Ried, Ka Ho Wong
Calendar:
Time: 4:30-5:30pm
Location: KT 801
Abstract: In recent and upcoming work joint with Anna Wienhard, Zach Greenberg and Merik Niemeyer, we describe a large class of Lie groups as simpler Lie groups “defined over noncommutative rings”, the simplest example expresses the symplectic group SP_2n as as SL_2 over a matrix ring. We use this description to construct cluster coordinates on moduli spaces of G local systems on surfaces decorated by partial flags of G at the punctures of S. The cluster algebras and varieties which arise this way are noncommutative versions of those coming from Fock and Goncharov cluster coordinates associated to the split Lie group and full flags of this simpler type. I will give an overview of this theory and give an outlook towards some new perspectives on cluster quantization.
Time: 4:30-5:30pm
Location: KT 801
Abstract: According to the Gaiotto–Moore–Neitzke algorithm, spectral networks associated to differentials on Riemann surfaces can be used to compute the BPS states of certain supersymmetric quantum field theories. The construction of spectral networks associated with cubic differentials admits a particularly simple description in terms of flat geometry: they appear as graphs of straight trajectories that generate new ones upon intersection under certain conditions. We present the notion of spectral core as a refinement of the classical core concept by Haiden, Katzarkov, and Kontsevich in flat surface theory, and show that it precisely controls the birthing process of spectral networks trajectories. As an application, we describe the spectral networks corresponding to polynomial cubic differentials of degree d=3. Time permitting, we will also discuss the problem of characterizing cubic differentials whose associated spectral networks generated by the algorithm have finite complexity. This work is a collaboration with Omar Kidwai.
Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
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Time: 4:30-5:30pm
Location: KT 801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT 801
Abstract: TBA
Time: 4:30-5:30pm
Location: KT 801
Abstract: TBA