Sebastian D. Melzer

Postdoctoral researcher
Department of Mathematics
University of Salerno
Email: greetings@skydivizer.com

About Me

I am a mathematician originally from Germany and raised in the Netherlands. I studied Computing Science (BSc) and Logic (MSc) at the University of Amsterdam, and completed my PhD in Mathematics at New Mexico State University. My research is centered on pointfree topology and duality theory, with a particular focus on Priestley duality as a way of understanding frames, locales, and related algebraic structures. What draws me to this area is how duality allows abstract, non-spatial objects to regain geometric meaning, and how ideas from topology, order theory, and logic continuously inform one another.

I am broadly interested in the interplay between different areas of mathematics and plan to continue this work as a postdoctoral researcher. Alongside research, I care deeply about clear and structured teaching, and about making difficult ideas feel intuitive without sacrificing precision. Outside academia, I enjoy video games, sports, and the occasional bad reality show. I also have a quiet but persistent fascination with national flags, learning to recognize them and remembering where they come from, a small reflection of my general love for patterns, structure, and visual languages. I have a particular weakness for chocolate-covered peanuts and a cold beer.

Biography

• 2025–2026: Postdoc at the Department of Mathematics at the University of Salerno
• 2021–2025: PhD and graduate assistant at the Department of Mathematical Sciences at New Mexico State University.
• 2018–2020: MSc Logic at the University of Amsterdam.
• 2015–2018: BSc Computing Science at the University of Amsterdam.
• Some time in the 20th century: Born in Tübingen, Germany.

Publications

Journal Papers

Preprints

1. Priestley perspective on pointfree topology with Guram Bezhanishvili. 2025. (view preprint)

Accepted

2. Local compactness does not always imply spatiality with Guram Bezhanishvili, Ranjitha Raviprakash, and Anna Laura Suarez. Questions Answers Gen. Topology, 2025. To appear. (view preprint)

Published

3. Maximal d-spectra via Priestley duality with Guram Bezhanishvili and Papiya Bhattacharjee. J. Algebra Appl., 2025. Online Ready. (view)
4. Algebraic frames in Priestley duality with Guram Bezhanishvili. Algebra Universalis, 81(1):25, 2025. (view)
5. Deriving dualities in pointfree topology from Priestley duality with Guram Bezhanishvili. Appl. Categ. Structures, 31(5):28, 2023. (view)
6. 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, November 2024, Mexico City, 🇲🇽. (slides: part 1, part 2, part 3)

Conference Talks

• Local compactness does not always imply spatiality. BLAST, May 2025, Boulder, Colorado, 🇺🇸. (slides)
• The maximal spectrum of d-elements is not always Hausdorff. TACL, July 2024, Barcelona, 🇪🇸. (slides)
• When is max(dL) Hausdorff? BLAST, April 2024, Denton, Texas, 🇺🇸. (slides)
• Priestley duality for d-frames. ITAC (El 56 Congreso de la Sociedad Matemática Mexicana), October 2023, San Luis Potosí, 🇲🇽 (online). (slides)
• Algebraic frames in Priestley duality. BLAST, May 2023, Charlotte, North Carolina, 🇺🇸. (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, 🇺🇸. (slides)
• Hofmann-Mislove through the lenses of Priestley. TACL, June 2022, Coimbra, 🇵🇹. (slides)
• Canonical formulas for IK4. BLAST, June 2021, Las Cruces, New Mexico, 🇺🇸 (online). (slides)

Seminar Talks

• Locally compact and sober, but not quite enough points. Seminar on Demain Theory and its Applications, December 2025, Tianyuan Mathematics Research Centre, Yunnan, 🇨🇳. (slides)
• Priestley duality for frames. Frame Theory Seminar, December 2024, Chapman University, Orange, California, 🇺🇸. (slides)
• Topics in Pointfree Topology: Duality Theorems. Foundations Seminar, November 2022, New Mexico State Universty, Las Cruces, New Mexico, 🇺🇸.
• Canonical Formulas for the Lax Logic. TULIPS, March 2021, University of Utrecht, 🇳🇱 (online). (slides)

Defenses

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

Teaching

Lecturer

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

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.