Siddharth Vadnerkar

Research Interests: 

I am interested in the rigorous study of gapped Symmetry Enriched Topological (SET) order from various lenses (with spin systems being my preferred way). My advisor is Bruno Nachtergaele.

SETs have a well developed algebraic theory from the perspective of tensor categories. This structure is conjectured to be robust under small perturbations. They also have microscopic lattice and field theory realisations. I am especially motivated by questions involving extraction of interesting macroscopic data from various exactly solvable lattice models hosting SET phases, neatly arranging this data in an algebraic format, and showing its robustness under small perturbations.

My research has strong connections to topological quantum computing, which is a field that perform quantum computation using local operations on anyons and defects. For example, Fibonacci anyons are capable of realising a universal gate set via braiding of anyons, and as another example, symmetry defects in the Z_2 enriched Toric Code serve as a realisation of a Hadamard gate.

Current news about me:

Mar '25: My new paper (totally not counting anymore) arxiv: https://arxiv.org/abs/2503.15611
Mar '25: March meeting time. My first one. So many great people, and gave a presentation and poster on my previous paper! slides.
Nov '24:  My  fourth paper!  I will definitely stop counting after this one ;)  arxiv: https://arxiv.org/abs/2410.23380
Oct '24: Gave a seminar talk at BIMSA on "Extracting symmetry fractionalisation data from microscopics" here are the slides.
Aug '24:  Visited DAMTP quantum information group and University of Oxford for Symmetries 24
July '24:  Visited CU Boulder for the $C^*$-algebras in spin systems summer school. Lovely place!
Nov '23: My third paper! I really should stop counting... arxiv link: https://arxiv.org/abs/2310.19661
Aug '23: Attended the workshop Paths to QFT 2023, Durham and met some great researchers.
Aug '23: Gave a seminar at Cambridge University for the TCM group on the Dynamic Toric Code Model.
Aug '23: Published my second paper! Here is the arxiv link: https://arxiv.org/abs/2308.06883
July '23: Visited PSSCMP 2023 and presented a poster based on the "Dynamic Toric Code Model".
Mar '23: Published my first paper! Here is the arxiv link: https://arxiv.org/abs/2303.07379
Jan '23: Gave an informal talk on "Superselection sectors in the 3d Toric Code". Here is the recording.
Jan '23:  Invited to speak on "Topology in physics" at the physics department colloquium at UC Davis. Here are the slides.
Sept '22: Attended the "Generalised Global Symmetries" summer conference at the Simons Center. Had an excellent time learning about the applications of UMTCs in HEP/Condensed Matter.
Sept '22: Gave a talk at QMATH15 on "Dynamic Toric Code Model". Here are the slides.
June '22: Gave a talk at GLaMP '22 on "Dynamic Toric Code model". Here are the slides.
Sept '21: Attended the "Mathematics of Topological Phases of Matter" summer school, and met some great researchers.
May '21: Passed my qualifying exam! Now I can look forward to publishing with the blessings of the university.
Feb '20: Gave a talk in the "Quantum Lattice Systems" seminar series on my current research, the "Dynamic Toric Code Model".
Sept '20: Gave a talk in a seminar series "Quantum Lattice Systems" on "Chern Simons theory and topology in higher dimensions" hosted by Professor Martin Fraas.