Email 1: dsoskin at math dot ucla dot edu
Email 2: dssoskin at gmail dot com
Address: MS 6236, UCLA
520 Portola Plaza,
Los Angeles, CA 90095
Photo credit: Andrea Kane, Institute for Advanced Study
I am an Assistant Adjunct Professor at UCLA working with
Igor Pak, July 2025 - July 2026.
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I was a Member at School of Mathematics at Institute for Advanced Study working with June Huh,
September 2024-July 2025.
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I was a C.C. Hsiung Visiting Assistant Professor at Lehigh University under the supervision of Mark Skandera,
August 2023 - July 2024.
I have received a PhD degree in the Department of Mathematics of The University of Notre Dame in South Bend, Indiana (2017-2023). I was extremely lucky to be a graduate student of Michael Gekhtman.
My research interests lie at the intersection of algebra and combinatorics. I am particularly interested in problems related to positivity phenomena in algebraic combinatorics, rep. theory, cluster algebras. My studies are centered around inequalities arising from real algebraic geometry and tropical geometry which I aim to understand from combinatorial and computational complexity viewpoint. ​​​​
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11. “Bounded ratios for Lorentzian matrices”, with Daoji Huang, June Huh and Botong Wang, in progress.
Publications and preprints
Results on bounded ratios is a featured topic in Arbeitsgemeinschaften at Oberwolfach, Oct. 2025.
10. “Schur inequalities and Littlewood–Richardson coefficients”, joint with Igor Pak, in progress
9. Hadamard product of dual Jacobi–Trudi matrices”, with Robert Angarone, Jang Soo Kim and Jaeseong Oh, in progress
8. “Bounded Ratios and Convergence of String Integrals”, with Nick Early, Michael Gekhtman, in progress
7. “Cluster multiplicative inequalities in finite type cluster algebras”, joint with Zachary Greenberg and Michael Gekhtman, arXiv:2409.06642 (2024), accepted to Algebraic Combinatorics
6. “Generalized diagonals in positive semi-definite matrices”, joint with Robert Angarone,
in European Journal of Combinatorics, Vol. 130, (2025)
4. “Plücker inequalities for weakly-separated coordinates in totally nonnegative Grassmannians”, joint with Prateek Kumar Vishwakarma, arXiv:2310.12916 (2023), submitted, poster at FPSAC’25
3. “Barrett-Johnson inequalities for totally nonnegative matrices”, joint with Mark Skandera, Linear and Multilinear Algebra, Volume 73, 2025, Issue 10, pp. 2320-2343, shorter version in S´eminaire Lotharingien de Combinatoire 89B, Article 29
2. “On bounded ratios of minors of totally positive matrices”, joint with Michael Gekhtman,
in Linear Algebra and its Applications, Volume 715, 2025, pp. 46-67
Talks
26. “Multiplicative inequalities for cluster algebras of finite type”, Workshop on Matrices and Operators, University of Regina, (on Zoom), 2025
25. “Multiplicative inequalities for cluster algebras of finite type”, Mathematical Congress of the Americas 2025
24. “Multiplicative inequalities for cluster algebras of finite type”, Institute for Advanced Study, USA, 2025
23. “Multiplicative inequalities for cluster algebras of finite type”, Canadian Mathematical Society (CMS) Summer Meeting, (on Zoom), 2025
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22. "Equalities and Inequalities on Products of Schur functions”, Institute for Advanced Study, USA, 2025
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21. “Multiplicative inequalities for totally positive matrices”, MIT, USA, 2025
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20. “Total positivity and determinantal inequalities”, UCLA, USA, 2024
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19. “Total positivity and determinantal inequalities”, Institute for Advanced Study, USA, 2024
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18. “Cluster multiplicative inequalities on positive locus”, Lehigh University, USA, 2024
17. “Multiplicative and additive determinantal inequalities for totally nonnegative matrices”, Yale University, USA, 2023
16. “Multiplicative and additive determinantal inequalities for totally nonnegative matrices”, University of Michigan, USA, 2023
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15. “Multiplicative and additive determinantal inequalities for totally nonnegative matrices”, UC San Diego, USA, 2023
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14. “Barrett-Johnson inequalities for totally nonnegative matrices”, AMS Special Session on Cluster Algebras, Positivity and Related Topics, Cincinnati, USA, 2023
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13. “Determinantal inequalities for totally positive matrices”, Regina University, Canada, 2023 (on Zoom)
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12. “Determinantal inequalities for totally positive matrices”, University of Leeds, UK, 2022
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11. “Determinantal inequalities for totally positive matrices”, Rutgers University, USA, 2022
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10. “Determinantal inequalities for totally positive matrices”, PCU of Rio de Janeiro, Brazil, 2022 (On Zoom)
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9. “Determinantal inequalities for totally positive matrices”, Michigan State University, USA, 2022
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8. “Determinantal inequalities for totally positive matrices”, University of Minnesota, USA, 2022
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7. “Determinantal inequalities for totally positive matrices”, University of Pennsylvania, USA, 2022
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6. “Determinantal inequalities for totally positive matrices”, Lehigh University, USA, 2022
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5. “Determinantal inequalities for totally positive matrices”, University of Notre Dame, USA, 2022
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4. “Lie algebras and Dynkin diagrams”, Heidelberg University, Germany, 2022
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3. “Skein and cluster algebras of marked surfaces”, University of Notre Dame, USA, 2021
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2. “Dimers and cluster integrable systems”, University of Notre Dame, USA, 2019
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1. “Arrangements of equal minors in the positive grassmannian”, University of Notre Dame, USA, 2019
Teaching
Primary Instructor, Algorithms, Fall 2025 (one class)
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Primary Instructor, Introduction to Discrete Structures, Fall 2025 (one class)
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Instructor, Calculus II, Spring 2024 (one class)
Primary Instructor, Survey of Calculus II, Summer 2024 (one class)
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Instructor, Calculus I, Fall 2023 (two classes)
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Instructor, Research Experience for Undergraduates, Summer 2022 (one class)
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Instructor, Calculus II, Spring 2020 (one class)
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Teaching Assistant, Linear Algebra and Differential Equations, Spring 2023 (one class)
Teaching Assistant, Calculus I, Fall 2018, Fall 2019, Fall 2020 (seven classes)
Teaching Assistant, Calculus II, Spring 2019, Fall 2021, Spring 2022 (five classes)
Teaching Assistant, Calculus III, Spring 2021 (two classes)