Dheeran E. Wiggins

Email: dheeran2@illinois.edu
Pronunciation: Dheeran (dee-rin) Eugene (yu-jeen) Wiggins (wig-ins)
Curriculum Vitae
ORCID: 0000-0001-6996-1406

I am a fourth-year mathematics undergraduate at the University of Illinois. Recently, field theory with defects and related \(n\)-categorical quantum things have my attention. This page is where I house my teaching materials, expository writing, various notes, and talks.

I am working with Graeme Smith at the Institute for Quantum Computing at the University of Waterloo in the summer of 2026, after spending a week at the Atlantic TQFT Spring School at Dalhousie University. I also made my way over to the Summer School on Homotopy Colimits at the University of Regina.

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.

I am a signatory of the Leiden Declaration and a firm believer in human mathematics. My beliefs are summarized by the following.

The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians. — Peter Scholze

Notes

• Math 506: Group Representation Theory (Andy Hardt; in progress)
  character theory, \(\operatorname{Ind}_H^G \dashv \operatorname{Res}_H^G \), Specht modules, \(\mathfrak{s}\mathfrak{l}_2 \mathbb{C}\), root systems, highest weight representations, Peter-Weyl theorem, quivers, quantum groups
• Math 503: Geometric Group Theory (Igor Mineyev; in progress)
  Cayley graphs \(\Gamma(G,S)\), Nielsen transformations, Stallings immersions, SHNC, Marshall Hall's theorem, quasiisometry, \(\operatorname{CAT}(\kappa)\), hyperbolicity
• 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, \(\operatorname{Bun}_G(M)\) and 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, \(\operatorname{Cat}_{\infty}\), \(\pi_n : \operatorname{Kan}_* \to \operatorname{Set}_*\), 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, \(\operatorname{Grp}\), actions, \(\operatorname{Set}_G\), group rings, domains, \(\operatorname{Mod}_R\), 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, \(\pi_1: \operatorname{Top}_{*} \to \operatorname{Grp}\)
• ECE 498: Quantum Information Processing Theory (Eric Chitambar)
  state spaces, tensor products, \(\operatorname{SU}(2)/C_2 \simeq \operatorname{SO}(3)\), 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, \(L^p(E,d \mu)\)

Talks

• May 2026 Some (semi)simple things about 2D unitary TQFT with defects at the MathQuantum Annual Symposium.
• Apr 2026 Unitary field theories with defects in two dimensions at the Illinois Undergraduate Research Symposium.
• Mar 2026 Locality via (co)limits in an infinite spin chain at the Rose-Hulman Undergraduate Mathematics Conference. Joint with Igor Mineyev.
• Mar 2026 Stabilizer formalism in \(\infty\)-qubit systems at the American Physical Society Global Physics Summit. Joint with Igor Mineyev.
• 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 Karnataka GEM 014. I keep a log here.
• Self-study: I am slowly working through
  • Lectures on Field Theory and Topology by Dan Freed.
  • Tensor Categories by Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik.
  • Spectra and stable homotopy theory by Cary Malkiewich.
  • More Concise by Peter May and Kate Ponto.
• Reading: I have been enjoying Dubliners by James Joyce, and I am always open to suggestions for my next read. 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 money tree and a lucky "bamboo."