Dheeran E. Wiggins

I am a second-year mathematics undergraduate at the University of Illinois studying algebra, topology, and quantum information. Recently, monoidal categories (e.g., \(\textsf{Hilb}, \textsf{Mod}_R, \textsf{Rel}\)) and categorical quantum theory have my attention.

Teaching

Papers

Notes

I take my notes live in \(\LaTeX\), largely to motivate myself to attend lecture. These will likely have mistakes or missing proofs, depending upon my attentiveness on a given day.

Math 527: Homotopy Theory (Charles Rezk; in progress)
Math 525: Algebraic Topology I (James Pascaleff; in progress)
Math 425: Honors Advanced Analysis (Burak Erdogan; in progress)
Math 501: Abstract Algebra II (Igor Mineyev; in progress)
MATH 500: Abstract Algebra I (Charles Rezk)
free groups, \(\textsf{Grp}\), actions, \(\textsf{Set}_G\), group rings, domains, \(\textsf{Mod}_R\), coproducts, semisimple rings, modules over PIDs, fields, Galois correspondence
MATH 535: General Topology (Igor Mineyev)
homeomorphisms, invariants, \(\ell^p(\mathbb{N}, \mathbb{R})\), separability, embeddings, \(Y^X\), \(\mathcal{B}(X,Y) \), \(\mathcal{C}(X,Y)\), completions, \(\pi_1: \mathsf{Top}_{*} \to \mathsf{Grp}\)
ECE 498: Quantum Information Processing Theory (Eric Chitambar)
state spaces, tensor products, \(\operatorname{SU}(2) \simeq \operatorname{SO}(3)\), CPTP channels, Pauli twirling, POVMs, LOCC, teleportation, nonlocality
MATH 418: Intro to Abstract Algebra II (Andy Hardt)
domains, \(R[x]\) irreducibility, fields and towers, \(\operatorname{Gal}(\mathbb{K}/\mathbb{L})\), \(\mathbb{C}\mathrm{P}^n\), projective and affine Nullstellensatz
MATH 424: Honors Real Analysis (Eugene Lerman)
topology, metric spaces, differentiation, integration, interchange of limit operations, Lebesgue measure and integration, \(L^1(E,d \mu)\)

Talks & Posters

May 2024 Winter Spaces and the Stabilizer Formalism at the Illinois Mathematics Lab Open House with Anderson et al. Poster advised by Roy Araiza.
Apr 2024 Modeling a Viral Epidemic With a Concurrent ''Misinfodemic'' at the Research Institute Spring Scientific Research Poster Reception. Poster advised by Anthony Solomonides.
Apr 2024 Modeling a Viral Epidemic With a Concurrent ''Misinfodemic'' at the Illinois Undergraduate Research Symposium. Talk advised by Anthony Solomonides.
Apr 2024 Winter Spaces and the Stabilizer Formalism at the Illinois Quantum Information Science & Technology (IQUIST) World Quantum Day with Anderson et al. Poster advised by Roy Araiza.
Apr 2023 Identification and estimated yield of background events in a search for doubly charged Higgs bosons at CMS at the American Physical Society April Meeting with Anne et al. Poster advised by Peter Dong.
Apr 2023 Identification of optimal production channels for dark photon searches at the American Physical Society April Meeting with Anne et al. Poster advised by Peter Dong.
Apr 2023 Unidirectional build architecture: Refactoring a HEP data collection codebase at the Annual IMSAloquium. Talk advised by Peter Dong.
Apr 2022 An investigation of triboson decays into four-lepton final states at the Annual IMSAloquium with George Bayliss and Jesus Fileto. Talk advised by Peter Dong.

Lately

Coffee: Most mornings I use the Fellow Ode Gen 2 with a classic ceramic V60. At the moment I am drinking Dancing Goats Ethiopia Sidamo Guji.
Self-study: I am slowly working through
- homotopy type theory (HoTT) with Anthony Solomonides.
- Casson's Invariant for Oriented Homology Three-Spheres: An Exposition by Selman Akbulut and John McCarthy.
- Categories for Quantum Theory: An Introduction by Jamie Vicary and Chris Heunen.
Reading: When I have time, I pick up A History of Western Philosophy by Bertrand Russell. I regret not spending more of my daylight in a book, though.