Sebastian D. Melzer

Postdoctoral researcher
Department of Mathematics
University of Salerno

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About Me

I am a mathematician/logician originally from Germany and raised in the Netherlands. I studied Computing Science (BSc) and Logic (MSc) at the University of Amsterdam, and did 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 and related algebraic structures.

Alongside research, I care about structured and meaningful teaching, particularly about making abstract ideas feel meaningful. The ways in which my teachers presented and engaged with their material have had a great impact on my life. In my opinion, more important than proving a difficult result is being able to interpret it in a meaningful way. This is a skill that I unfortunately still seem to not have mastered.

Outside academia, I enjoy video games, sports, and the occasional tv show. I have a particular weakness for chocolate-covered peanuts (choco pinda’s).

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

Accepted

1. Local compactness does not always imply spatiality with Guram Bezhanishvili, Ranjitha Raviprakash, and Anna Laura Suarez. Questions Answers Gen. Topology, 2026. To appear. arXiv

Published

2. Maximal d-spectra via Priestley duality with Guram Bezhanishvili and Papiya Bhattacharjee. J. Algebra Appl., 2027. Online Ready. PDFDOI
3. Algebraic frames in Priestley duality with Guram Bezhanishvili. Algebra Universalis, 86:6, 2025. PDFarXivDOI
4. Deriving dualities in pointfree topology from Priestley duality with Guram Bezhanishvili. Appl. Categ. Structures, 31:34, 2023. PDFarXivDOI
5. Hofmann-Mislove through the lenses of Priestley with Guram Bezhanishvili. Semigroup Forum, 105:825-833, 2022. PDFarXivDOI

Submitted

• When is double negation Scott continuous? with Guram Bezhanishvili. 2026. arXiv
• Maximal d-spectra and locally compact Hausdorff spaces with Guram Bezhanishvili, Papiya Bhattacharjee, and M. Drew Moshier. 2026. arXiv
• A choice-free approach to Wallman compactifications with Cerene Rathilal and Ranjitha Raviprakash. 2026. arXiv
• Priestley perspective on pointfree topology with Guram Bezhanishvili. 2025. arXiv

Theses

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

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.

Talks