Dheeran E. Wiggins

I am a third-year mathematics undergraduate at the University of Illinois studying algebra, topology, and quantum information. Recently, monoidal categories (e.g., \(\textsf{Hilb}, \textsf{Rep}_G, \textsf{Bord}_d\)) and categorical quantum things have my attention. This page is where I house my teaching materials, expository writing, various notes, and talks.

During the summer of 2025, I became a MathQuantum Fellow at the University of Maryland, College Park. In August, I was at the Summer School on Geometry, hosted by the Utrecht Geometry Centre at Universiteit Utrecht. I have begun keeping an academic travelogue.

Teaching

Expository

Notes

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

Math 595: Representation-theoretic Methods in QIT (Felix Leditzky; in progress)
Werner states, Schur-Weyl duality, irreducibles of \(\mathcal{U}_d\) and \(S_n\), isotropic states, de Finetti theorem, approximate cloning, spectrum estimation
Math 595: Topological Field Theories in 2D (James Pascaleff; in progress)
Atiyah-Segal axioms, Frobenius algebras, \(\operatorname{Bun}_G(M)\), 2D Dijkgraaf-Witten theory, conformal structures, TCFTs, CohFTs, Gromov-Witten theory
Math 526: Algebraic Topology II (Jeremiah Heller; in progress)
universal coefficients, \(\lim^1\), Milnor sequence, cup products, acyclic models, Steenrod squares, Poincaré duality, vector bundles, Stiefel-Whitney classes
Pontryagin-Thom Construction (Gijs Heuts, Miguel Barata)
regular values, framed submanifolds, homotopy groups \(\pi_n X \), stabilization, cobordisms, Hopf fibration, cobordism groups \(\Omega_k^{\mathrm{f}}\), Pontryagin-Thom
Matrix Lie Groups (Douwe Hoekstra, Sven Holtrop)
matrix exponentials and logarithms, matrix lie groups, Lie algebras, Baker-Campbell-Hausdorff, Lie subgroups, Lie subalgebras, Lie's Third Theorem
Math 527: Homotopy Theory (Charles Rezk; notes in progress)
nerves, \(\infty\)-categories, fibrations, anodyne, slices, Joyal lifting, \(\mathsf{Cat}_{\infty}\), \(\pi_n : \mathsf{Kan}_* \to \mathsf{Set}_*\), presentability, stability, spectra, operads
Math 525: Algebraic Topology I (James Pascaleff; notes in progress)
homotopy, \(\pi_1(X,x_0)\), covering spaces, lifting, CW complexes, \(\Delta\)-complexes, Galois covers, singular and cellular homology, Eilenberg-Steenrod axioms
MATH 501: Abstract Algebra II (Igor Mineyev)
categories, (co)limits, \(\operatorname{Hom}\) and \(\otimes_R\), adjunctions, (co)homology, \(\operatorname{Tor}_n^R\) and \(\operatorname{Ext}^n_R\), spectral sequences, multilinear algebra, representations
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, constructability, \(\operatorname{Gal}(\mathbb{K}/\mathbb{L})\), Galois correspondence, solvability, \(\mathbb{C}\mathrm{P}^n\), 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

Apr 2025 A model for the infinite tensor product of groups: Insights from quantum information at the Illinois Undergraduate Research Symposium. Talk advised by Igor Mineyev.
Mar 2025 On noncommutative graphs and Poulin's stabilizer formalism at the Rose-Hulman Undergraduate Mathematics Conference. Talk advised by Roy Araiza.
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 Counter Culture Valle Inca.
Self-study: I am slowly working through
- Tensor Categories by Dmitri Nikshych, Pavel Etingof, and Shlomo Gelaki.
- Modern Classical Homotopy Theory by Jeffrey Strom.
- More Concise by Peter May and Kate Ponto.
- Handbook of Categorical Algebra 2: Categories and Structures by Francis Borceux.
- Theory of Operator Algebras I by Masamichi Takesaki.
Reading: I recently started Stoner by John Williams. When I find time, the next on my list will be Dubliners by James Joyce. I regret not spending more of my daylight in a book, though.
Plants: Besides my collection of mostly hydroponic pothos, I have been tending to a new money tree and a lucky "bamboo." I also like to keep some English ivy around.