6 citations · 38 across the 44 of their papers we have counts for
55 papers
Nilpotent representations over equioriented cyclic quivers
Cornell Holmes, Mee Seong Im
We give a geometric description of nilpotent representations of equioriented cyclic quivers over a field via an explicit bijection. Over a finite field, this yields formulas for th…
Multisymmetric polynomials on set-theoretic quiver representations
Radford Green, Cornell Holmes, Mee Seong Im
Eventually constant set-valued representations of a quiver are set-theoretic analogues of nilpotent representations. In recent work by Green-Holmes-Im, the authors enumerated event…
Multisymmetric functions on eventually constant cyclic graphs
Radford Green, Cornell Holmes, Mee Seong Im
The study of spanning trees and related structures is central in graph theory, closely connected to understanding functions between finite sets. This paper generalizes the establis…
Eventually constant maps for two sets and nilpotent pairs
Weixi Chen, Mee Seong Im, Catherine Lillja +1
We give a bijective correspondence between the number of nilpotent matrices over a Boolean semiring and the number of directed acyclic graphs on ordered vertices. We then enumerate…
Pairs of eventually constant maps and nilpotent pairs
Weixi Chen, Mee Seong Im, Mikhail Khovanov +2
Tom Leinster gave a bijective correspondence between the set of operators on a finite-dimensional vector space and the set of pairs consisting of a nilpotent operator and a vec…
Two-dimensional topological quantum field theories of rank two over Dedekind domains
Fabian Espinoza, Mee Seong Im, Mikhail Khovanov
We give examples of Frobenius algebras of rank two over ground Dedekind rings which are projective but not free and discuss possible applications of these algebras to link homology…
Diagrammatics of information
Mee Seong Im, Clement Kam, Caden Pici
We introduce a diagrammatic perspective for Shannon entropy created by the first author and Mikhail Khovanov and connect it to information theory and mutual information. We also gi…
Entropy, cocycles, and their diagrammatics
Mee Seong Im, Mikhail Khovanov
The first part of the paper explains how to encode a one-cocycle and a two-cocycle on a group with values in its representation by networks of planar trivalent graphs with edge…
Foams with flat connections and algebraic K-theory
David Gepner, Mee Seong Im, Mikhail Khovanov +1
This paper proposes a connection between algebraic K-theory and foam cobordisms, where foams are stratified manifolds with singularities of a prescribed form. We consider -dimen…
Foam cobordism and the Sah-Arnoux-Fathi invariant
Mee Seong Im, Mikhail Khovanov
This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is pro…
Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words
Paul Gustafson, Mee Seong Im, Mikhail Khovanov
Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where…
From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions
Mee Seong Im, Mikhail Khovanov
This is a brief introduction to link homology theories that categorify Reshetikhin--Turaev -quantum link invariants. A recently discovered surprising connection bet…
Universal construction in monoidal and non-monoidal settings, the Brauer envelope, and pseudocharacters
Mee Seong Im, Mikhail Khovanov, Victor Ostrik
This paper clarifies basic definitions in the universal construction of topological theories and monoidal categories. The definition of the universal construction is given for vari…
Automata and one-dimensional TQFTs with defects
Paul Gustafson, Mee Seong Im, Remy Kaldawy +2
This paper explains how any nondeterministic automaton for a regular language gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoi…
One-dimensional topological theories with defects: the linear case
Mee Seong Im, Mikhail Khovanov
The paper studies the Karoubi envelope of a one-dimensional topological theory with defects and inner endpoints, defined over a field. It turns out that the Karoubi envelope is det…
Computational complexity reduction of deep neural networks
Mee Seong Im, Venkat R. Dasari
Deep neural networks (DNN) have been widely used and play a major role in the field of computer vision and autonomous navigation. However, these DNNs are computationally complex an…
Topological theories and automata
Mee Seong Im, Mikhail Khovanov
The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite stat…
Foams, iterated wreath products, field extensions and Sylvester sums
Mee Seong Im, Mikhail Khovanov
Certain foams and relations on them are introduced to interpret functors and natural transformations in categories of representations of iterated wreath products of cyclic groups o…
Natural transformations between induction and restriction on iterated wreath product of symmetric group of order
Mee Seong Im, Can Ozan Oğuz
Let be the group algebra of -step iterated wreath product. We prove some structural properties of $\mathsf{A}…
One-dimensional topological theories with defects and linear generating functions
Mee Seong Im, Paul Zimmer
We study the Gram determinant and construct bases of hom spaces for the one-dimensional topological theory of decorated unoriented one-dimensional cobordisms, as recently defined b…
Irreducible components of two-row Springer fibers for all classical types
Mee Seong Im, Chun-Ju Lai, Arik Wilbert
We give an explicit description of the irreducible components of two-row Springer fibers for all classical types using cup diagrams. Cup diagrams can be used to label the irreducib…
A study of irreducible components of Springer fibers using quiver varieties
Mee Seong Im, Chun-Ju Lai, Arik Wilbert
It is a remarkable theorem by Maffei--Nakajima that the Slodowy variety, which is a subvariety of the resolution of the nilpotent cone, can be realized as a Nakajima quiver variety…
Genetic optimization algorithms applied toward mission computability models
Mee Seong Im, Venkat R. Dasari
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the best species to survive. They are heuristics based and low cost…
Towards the affine and geometric invariant theory quotients of the Borel moment map
Mee Seong Im, Meral Tosun
We study the Borel moment map , given by , and describe our algorithm to construct th…