Mee Seong Im

Mathematics is the most beautiful and most powerful creation of the human spirit. 

Stefan Banach

Curriculum Vitae                      Curriculum Vitae (medium length)

ResearchGate ORCID Google Scholar

Zentralblatt MATH Math Reviews                      Mathematics Genealogy

Background

• Doctor of Philosophy (Ph.D.) in Mathematics at the University of Illinois at Urbana-Champaign

• Master of Arts (M.A.) in Mathematics at the University of Georgia

• Master of Philosophy (M.Phil.) in Mathematics at the University of Birmingham, England

• Bachelor of Science (B.S.) in Physics at the University of Georgia

• Bachelor of Science (B.S.) in Mathematics at the University of Georgia

In Fall of 2024, I am teaching  Math 608 Riemann Surfaces.

Special Geometric Representation Theory Session:  I am organizing a special session Geometric and topological aspects of mathematical physics and representation theory to be held in May 16-18, 2025 at the University of Wisconsin at Madison, WI with Xin Jin and Xinchun Ma.

Knots in Washington 50:  I am organizing Knots in Washington 50 at George Washington University, Washington, DC, joint with Valentina Harizanov, Mikhail Khovanov, Józef Przytycki, and Radmila Sazdanovic. It will be held in December 6-8, 2024.

Journal of Pure and Applied Algebra:  Jon Kujawa (Oregon State University),  Julia Pevtsova (University of Washington),  Milen Yakimov (Northeastern University), and I are putting together a special issue.  More details to follow.

Contemporary Mathematics:  Alessandro Arsie (University of Toledo),  Elira Curri (Oakland University),  Tony Shaska (Oakland University), and I are putting together AMS's Contemporary Mathematics volume Recent Advances in Mathematics and Artificial Intelligence for the sectional meeting in April 2024 at the University of Wisconsin-Milwaukee.

Research Interests

• Geometric and topological aspects of (Grothendieck-)Springer fibers.  Equivariant geometry, quiver flag varieties, Hilbert schemes and moduli constructions.

• Topological quantum field theories (TQFTs) and related areas, and categorification.  Connections of TQFT to number theory, mathematical physics, K-theory, dynamical systems, algebraic geometry.

• Representations of Lie superalgebras.  Combinatorial, categorical, and geometric connections to Lie superalgebras.

Keywords:  geometric and categorical representation theory;  Lie superalgebras;  quantum topology;  topological quantum field theories.

Publications, arXiv

Work in Progress.

1. On a certain bases of Lie superalgebra (tentative title), in progress. 

2. On cohomological properties of quiver flag varieties (tentative title), in progress.  

3. Certain holomorphic line bundles (tentative title), with M. Zakrzewski, in progress, 2024. 

4. On certain Lie superalgebras (tentative title), with E. Norton and B. Westbury, in progress, 2024.

5. On certain invariants of a Lie superalgebra (tentative title), in preparation, 2024. 

6. Quantum groups and colored HOMFLY-PT invariants (tentative title), in preparation, 2024. 

7. On certain properties of the periplectic Lie superalgebra (tentative title), with Shifra Reif, in progress, 2024. 

8. TBA, with Mikhail Khovanov and Victor Ostrik, in progress, 2024.

9. TBA, with Mikhail Khovanov, Louis-Hadrien Robert, Joshua Sussan, and Pedro Vaz, in progress, 2024.

10. TBA, with Mikhail Khovanov and Anton Zeitlin, in progress, 2024.

11. Algebraic number theory and monoidal categories, with Mikhail Khovanov, in progress, 2024.

12. Ubiquity of universal construction and cobordisms everywhere, with Mikhail Khovanov, in progress, 2024.

13. Projective modules and topological quantum field theory, with Mikhail Khovanov, in-preparation, 2024.

14. Boolean topological theories and multiplicative graph invariants, with Mikhail Khovanov, in-preparation, 2024.

15. Quasicharacters and graph topological theories, with Mikhail Khovanov and Joshua Sussan, in progress, 2024. 

16. Automata and finite-state machines with boundary, with Mikhail Khovanov, in-preparation, 2024.

17. Monoidal categories and diagrammatics of group cocycles in low degrees II: The multiplicative case, with Mikhail Khovanov, in progress, 2024.

18. Distributive and nondistributive lattices, with Remy Kaldawy, Mikhail Khovanov, and Zachary Adam Lihn, in-preparation, 2024.

19. TBA, with Mark Ebert and Alvaro L. Martinez Ruiz, in progress, 2024.

20. TBA, with Mikhail Khovanov, Lev Rozansky, and Alexei Oblomkov, in progress, 2024.

21. TBA, with Mikhail Khovanov and Alexei Oblomkov, in progress, 2024.

22. TBA, with Neil Saunders and others, in progress, 2024.

23. TBA, with Mark Ebert, Mikhail Khovanov, Minh-Tâm Trinh, and Alvaro L. Martinez Ruiz, in progress, 2024.

24. TBA, with Fabian Espinoza and Mikhail Khovanov, in progress, 2024.

25. TBA, with Venkat Dasari, in progress, 2024.

Universal construction and monoidal categories.

26. Foam cobordisms and Igusa's homology groups, with Mikhail Khovanov, in preparation, 2024.

27. Diagrammatics of information, with Clement Kam and Caden Pici, submitted, Contemp. Math. (2024), 1-33. ⭐

28. Entropy, cocycles, and their diagrammatics, with Mikhail Khovanov, submitted, J. Pure Appl. Algebra (2024), 1-82. ⭐

29. Foams with flat connections and algebraic K-theory, with David Gepner, Mikhail Khovanov, and Nitu Kitchloo, submitted, Ann. K-Theory (2024), 1-57.  ⭐

30. Foam cobordism and the Sah-Arnoux-Fathi invariant, with Mikhail Khovanov, submitted, Arnold Math. (2024), 1-38.  ⭐

31. Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words, with Paul Gustafson and Mikhail Khovanov, accepted, Lett. Math. Phys. (2023), 1-32.  ⭐

32. From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions, with Mikhail Khovanov, accepted, Contemp. Math. (2023), 1-40.  ⭐

33. Universal construction in monoidal and non-monoidal settings, the Brauer envelope, and pseudocharacters, with Mikhail Khovanov and Victor Ostrik, submitted, Theory Appl. Categ. (2023), 1-59.  ⭐

34. Automata and one-dimensional TQFTs with defects, with Paul Gustafson, Remy Kaldawy, Mikhail Khovanov, Zachary Lihn, Lett. Math. Phys. 113 (2023), no. 93, 1-38.

35. One-dimensional topological theories with defects: the linear case, with Mikhail Khovanov, Contemp. Math. 791 (2024), 105-146. 

36. Topological theories and automata, with Mikhail Khovanov, submitted, Adv. Math. (2022), 1-70.

37. Foams, iterated wreath products, field extensions and Sylvester sums, with Mikhail Khovanov, accepted under revision, Theory Appl. Categ. (2021), 1-78.

38. One-dimensional topological theories with defects and linear generating functions, with Paul Zimmer, Involve, a Journal of Mathematics 15 (2022), no. 2, 319-331. 

Representation theory of Lie algebras and Lie superalgebras.

39. The Grothendieck ring of the periplectic Lie supergroup and supersymmetric functions, with Shifra Reif and Vera Serganova, submitted, Sém. Lothar. Combin. (2019), 1-12. 

40. Denominator identities for the periplectic Lie superalgebra, with Crystal Hoyt and Shifra Reif, J. Algebra 567 (2021), 459-474.

41. Irreducible calibrated representations of periplectic Brauer algebras and hook representations of the symmetric group, with Emily Norton, J. Algebra 560 (2020), 442-485. 

42. Grothendieck rings of periplectic Lie superalgebras, with Shifra Reif and Vera Serganova, Math. Res. Lett. 28 (2021), no. 4, 1175-1195. 

43. On calibrated representations of the degenerate affine periplectic Brauer algebra, with Zajj Daugherty, Iva Halacheva, and Emily Norton, Surv. Math. Appl. 16 (2021), 207-222.

44. The affine VW supercategory, with Martina Balagovic, Zajj Daugherty, Inna Entova, Iva Halacheva, Johanna Hennig, Gail Letzter, Emily Norton, Vera Serganova and Catharina Stroppel, Selecta Math. 26 (2020), no. 2, 42 pages.

45. Translation functors and decomposition numbers for the periplectic Lie superalgebra p(n), with Martina Balagovic, Zajj Daugherty, Inna Entova, Iva Halacheva, Johanna Hennig, Gail Letzter, Emily Norton, Vera Serganova and Catharina Stroppel, Math. Res. Lett. 26 (2019), no. 3, 643-710.

46. On Kostant's theorem for Lie algebra cohomology, with Brian D. Boe, Leonard Chastkofsky, Daniel K. Nakano, Jonathan R. Kujawa, Emilie Wiesner, Irfan Bagci, Benjamin Connell, Bobbe J. Cooper, Wenjing Li, Kenyon J. Platt, Caroline B. Wright, Ben Wyser and Tyler Kelly, Contemp. Math. 478 (2009), 39-60. 

Representation theory of finite groups and other algebras.

47. Natural transformations between induction and restriction on iterated wreath product of symmetric group of order 2, with Can Ozan Oguz, MDPI: Math. Physics 10 (2022), no. 20, 1-18.

48. A short proof on the transition matrix from the Specht basis to the Kazhdan-Lusztig basis, Rocky Mountain J. Math. 51 (2021), no. 5, 1671-1680.

49. Transitioning between tableaux and spider bases for Specht modules, with Jieru Zhu, Algebr. Represent. Theory 25 (2022), no. 2, 387-399. 

50. On the module structure of the center of hyperelliptic Krichever-Novikov algebras II, with Ben Cox, Xiangqian Guo, Kaiming Zhao, Comm. Alg. 47 (2019), no. 12, 5142-5163.

51. Categorification of Verma modules and indecomposable projective modules in the category I_g(sl(2)) for sl(2), with Ben Cox, accepted upon revision, Adv. Math. Sci. (2018), 29 pages.

52. On the module structure of the center of hyperelliptic Krichever-Novikov algebras, with Ben Cox, Representations of Lie Algebras, Quantum Groups and Related Topics, Contemp. Math. 713 (2018), 61-94.

53. Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence, with Angela Wu, Adv. Math. Sci. 15 (2018), 29-46.

54. Generalized iterated wreath products of cyclic groups and rooted trees correspondence, with Angela Wu, Adv. Math. Sci. 15 (2018), 15-28.

55. Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals, with Ben Cox, Integral Transforms Spec. Funct. 27 (2016), no. 11, 899-919.

Algebraic geometry, geometric representation theory, and differential geometry.

56. Irreducible components of two-row Springer fibers for all classical types, with Chun-Ju Lai and Arik Wilbert, Proc. Amer. Math. Soc. 150 (2022), no. 6, 2415-2432. 

57. A study of irreducible components of Springer fibers using quiver varieties, with Chun-Ju Lai and Arik Wilbert, J. Algebra 591 (2022), 217-248. 

58. Towards the affine and geometric invariant theory quotients of the Borel moment map, with Meral Tosun, accepted, Contemp. Math. (2020), 1-13. 

59. Suggestions to study affine and GIT quotients of the extended Grothendieck-Springer resolution, submitted, Surv. Math. Appl. (2019), 1-16.

60. Irreducible components of two-row Springer fibers and Nakajima quiver varieties, with Chun-Ju Lai and Arik Wilbert, preprint (2019), 1-38. 

61. The regularity of almost-commuting partial Grothendieck--Springer resolutions and parabolic analogs of Calogero--Moser varieties, with Travis Scrimshaw, J. Lie Theory 31 (2021), no. 1, 127-148. 

62. Beta super-functions on super-Grassmannians, with Michaƚ Zakrzewski, Lett. Math. Sci. 1 (2018), no. 1, 41-60. 

63. The regular semisimple locus of the affine quotient of the cotangent bundle of the Grothendieck-Springer resolution, J. Geom. Phys. 132 (2018), 84-98.

64. Unipotent invariants of filtered representations of quivers and the isospectral Hilbert scheme, with Lisa Jones, arXiv: 1608.02293, preprint (2016), 22 pages.

65. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution, IDEALS 2142 (2014), no. 49392, 1-134.

66. Semi-invariants of filtered quiver representations with at most two pathways, arXiv: 1409.0702, preprint (2014), 11 pages.

67. The regularity of the cotangent bundle of the Grothendieck-Springer resolution, article (2013), 3 pages. 

68. Examples relating to Green's conjecture in low characteristics and genera, with Topik Teguh Estu, Justin Manning, Zachary Michaels, Jason Pasko, William Rulla and Nishan Wijesinghe, accepted upon revision, Alg. Geom., MDPI (2022), 1-15.

Quantum programmable computers and related areas.

69. Computational complexity reduction of deep neural networks, with Venkat Dasari, Math. Militaris 25 (2022), no. 1, 1-10.

70. Genetic optimization algorithms applied toward mission computability models, with Venkat Dasari, 88th MORS Symposium: AI and Autonomous Systems WG35 (2020), 1-11. 

71. Monte Carlo methods on a fixed volume system of Silicon-Germanium atoms, Proc. SPIE 11410-29 (2020), 1-11. 

72. Solving machine learning optimization problems using quantum computers, with Lubjana Beshaj and Venkat Dasari, Proc. SPIE 11419-16 (2020), 1-10. 

73. Optimization problems with low SWaP tactical Computing, with Venkat Dasari, Lubjana Beshaj, and Dale Shires, Proc. SPIE 11013-G (2019), 1-8.

74. Complexity and mission computability of adaptive computing systems, with Venkat Dasari and Billy Geerhart, J. Defense Modeling & Simulation 17 (2019), no. 1, 1-7.

75. Optimization and synchronization of programmable quantum communication channels, with Venkat Dasari, Proc. SPIE 10660-26 (2018), 1-7.

Nonstandard analysis.

76. Nonstandard approach to Hausdorff outer measure, Math. Student 90 (2021), nos. 3-4, 159-171.

77. Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than 1, eTheses Repository 5218 (2005), 1-103.

Conference proceedings.

78. TBA, with Hanna E. Makaruk, Bach Nguyen, and Robert M. Owczarek, Contemporary Mathematics (2024), in-preparation.

79. Advances in the Mathematical Sciences, with Megan Breit-Goodwin, Kelly Jabbusch, and Kuei-Nuan Lin, Springer International Publishing Switzerland (2024), in-preparation.

80. Algebraic and Topological Aspects of Representation Theory, with Bach Nguyen and Arik Wilbert, Contemporary Mathematics 791 (2024), 1-227. 

81. Advances in the Mathematical Sciences, with Alyson Deines, Daniela Ferrero, Erica Graham, Carrie Manore, Candice Price, Springer International Publishing Switzerland 15 (2018), XIV, 1-270.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all. 

A Mathematician's Apology, by G. H. Hardy