Sebastian D. Melzer

Postdoctoral researcher

About Me

I am a mathematician originally from Germany, raised in the Netherlands. I completed a BSc in Computing Science and an MSc in Logic at the University of Amsterdam, followed by a PhD in Mathematics at New Mexico State University. My research lies at the intersection of pointfree topology, and duality theory with a focus on Priestley duality and its applications.

I am very interested in the interplay between different areas of mathematics and plan to continue this work as a postdoctoral researcher. Outside of academia, I enjoy video games, sports, and the occasional bad reality show. I also have a weakness for chocolate-covered peanuts and a cold beer.

Biography

Publications

Journal Papers

  • Local compactness does not always imply spatiality with Guram Bezhanishvili, Ranjitha Raviprakash, and Anna Laura Suarez. arXiv Preprint, 2025. (view)
  • Maximal d-spectra via Priestley duality with Guram Bezhanishvili and Papiya Bhattacharjee. arXiv Preprint, 2025. (view)
  • Algebraic frames in Priestley duality with Guram Bezhanishvili. Algebra Universalis, 81(1):25, 2025. (view)
  • Deriving dualities in pointfree topology from Priestley duality with Guram Bezhanishvili. Appl. Categ. Structures, 31(5):28, 2023. (view)
  • Hofmann-Mislove through the lenses of Priestley with Guram Bezhanishvili. Semigroup Forum, 105(3):825-833, 2022. (view)

Theses

  • Pointfree topology and Priestley duality. New Mexico State University, 2025. PhD Thesis. (view)
  • Canonical Formulas for the Lax Logic. University of Amsterdam, 2020. MSc Thesis. (view)
  • Thread-oriented program algebra. University of Amsterdam, 2018. BSc Thesis. (view)

Talks

Tutorials

  • Priestley duality and its applications to pointfree topology. MITAC'24, November 2024, Mexico City, Mexico. (slides: part 1, part 2, part 3)

Conference Talks

  • Local compactness does not always imply spatiality. BLAST'25, May 2025, Boulder, Colorado, United States. (slides)
  • The maximal spectrum of d-elements is not always Hausdorff. TACL'24, July 2024, Barcelona, Spain. (slides)
  • When is max(dL) Hausdorff?. BLAST'24, April 2024, Denton, Texas, United States. (slides)
  • Priestley duality for d-frames. ITAC (El 56 Congreso de la Sociedad Matemática Mexicana), October 2023, San Luis Potosí, Mexico (online). (slides)
  • Algebraic frames in Priestley duality. BLAST'23, May 2023, Charlotte, North Carolina, United States. (slides)
  • How to derive well-known dualities in point-free topology from Priestley duality. From Points to Neighborhoods and Beyond (AMS Special Session), September 2022, El Paso, Texas, United States. (slides)
  • Hofmann-Mislove through the lenses of Priestley. TACL'22, June 2022, Coimbra, Portugal. (slides)
  • Canonical formulas for IK4. BLAST'21, June 2021, Las Cruces, New Mexico, United States (online). (slides)

Seminar Talks

  • Priestley duality for frames. Frame Theory Seminar, December 2024, Orange, California, United States. (slides)
  • Topics in Pointfree Topology: Duality Theorems. Foundations Seminar, November 2022, Las Cruces, New Mexico, United States.
  • Canonical Formulas for the Lax Logic. TULIPS, March 2021, Utrecht, the Netherlands (online). (slides)

Defenses

  • Pointfree topology and Priestley duality. PhD Mathematics, March 2025, Las Cruces, New Mexico, United States. (slides)
  • Lax and steads wins the race. MSc Logic, December 2020, Amsterdam, the Netherlands (online). (slides)
  • Thread-Oriented Program algebra. BSc Computing Science, June 2018, Amsterdam, the Netherlands. (slides)

Teaching

Lecturer

  • Trigonometry and Pre-calculus, New Mexico State University, Spring 2025.
  • College Algebra, New Mexico State University, Fall 2024.
  • College Algebra, New Mexico State University, Spring 2024.
  • College Algebra, New Mexico State University, Fall 2023. (Notes)
  • College Algebra, New Mexico State University, Spring 2023.
  • College Algebra, New Mexico State University, Fall 2022.

Teaching Assistant

  • Introduction to Ordinary Differential Equations, New Mexico State University, Fall 2022.
  • Introduction to Real Analysis, New Mexico State University, Spring 2022.
  • Introduction to Higher Mathematics, New Mexico State University, Fall 2021.
  • Image Processing and Computer Vision, University of Amsterdam, Spring 2018.
  • Statistical Reasoning, University of Amsterdam, Spring 2018.
  • Discrete Mathematics and Logic, University of Amsterdam, Fall 2017. (Substitute)
  • Algorithms and Data Structures in Python, University of Amsterdam, Fall 2017.