Research Interests

Note: I am currently looking for industry partners for research projects. If you are interested, feel free to contact me informally by email.

Publications

Preprints

• P. Scheiblechner1, N. Correa Mañas, L. Plastina, M. Popovic, M. Egli, C. De Geyter, F. Ille, B. Leeners: Does follicular growth rate influence oocyte quality and treatment outcome in IVF/ICSI cycles?

Journal Publications

• M. Bilski, P. Scheiblechner: Effective approximation of the solutions of algebraic equations, Journal of Symbolic Computation 109: 144-176 (2022), arXiv:1603.07298.
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• Jana Koehler, Joseph Bürgler, Urs Fontana, Etienne Fux, Florian Herzog, Marc Pouly, Sophia Saller, Anastasia Salyaeva, Peter Scheiblechner, Kai Waelti: Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints, Constraints (2021/06/15), arXiv:2011.12862.
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• P. Scheiblechner: Effective de Rham Cohomology - The General Case, Communications in Contemporary Mathematics 21(05) (2019), arXiv:1203.5706.
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• J. Mittmann, N. Saxena, P. Scheiblechner: Algebraic Independence in Positive Characteristic: A p-adic Calculus, Transactions of the AMS 366(7): 3425-3450 (2014), arXiv:1202.4301.
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• P. Scheiblechner: Castelnuovo-Mumford Regularity and Computing the de Rham Cohomology of Smooth Projective Varieties, Foundations of Computational Mathematics 12(5): 541-571 (2012), arXiv:0905.2212.
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• P. Scheiblechner: On a Generalization of Stickelberger's Theorem, Journal of Symbolic Computation 45(12): 1459-1470 (2010).
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  Part of this paper was presented at MEGA 2009, Barcelona, Spain, June 15 - 19, 2009.
  
• P. Bürgisser and P. Scheiblechner: Counting Irreducible Components of Complex Algebraic Varieties, Computational Complexity 19(1): 1-35 (2010) (selected by the editors).
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• P. Bürgisser and P. Scheiblechner: On the Complexity of Counting Components of Algebraic Varieties, Journal of Symbolic Computation 44(9): 1114-1136 (2009).
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• P. Scheiblechner: On the Complexity of Deciding Connectedness and Computing Betti Numbers of a Complex Algebraic Variety, Journal of Complexity 23(3): 359-379 (2007).
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Conference Publications

• Jana Koehler, Joseph Bürgler, Urs Fontana, Etienne Fux, Florian Herzog, Marc Pouly, Sophia Saller, Anastasia Salyaeva, Peter Scheiblechner, Kai Waelti: Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints, 18th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research CPAIOR 2021, July 5 - 8, Vienna, Austria.
• P. Scheiblechner: Effective de Rham Cohomology - The Hypersurface Case, Proceedings of the 2012 International Symposium on Symbolic and Algebraic Computation, ISSAC 2012, arXiv:1112.2489.
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• P. Scheiblechner: On Lower Bounds for Algebraic Decision Trees over the Complex Numbers, Proceedings of the 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2010, presented in the special track Advances in the Theory of Computing 2010, Timisoara, Romania, September 23 - 26, 2010.
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• P. Scheiblechner: Comparison of Complexity over the Real vs. Complex Numbers, extended abstract, presented at Logical Approaches to Barriers in Computing and Complexity, Greifswald, Germany, February 17 - 20, 2010.
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• P. Bürgisser and P. Scheiblechner: Differential Forms in Computational Algebraic Geometry, Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, ISSAC 2007, 61 - 68, July 29 - August 1, Waterloo, Ontario, Canada.
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Book

P. Scheiblechner: Complexity of Counting Components of Algebraic Varieties - Irreducible and Connected Components, Betti Numbers VDM-Verlag Dr. Müller, 160 pp, paperback, ISBN 978-3-8364-9844-9

Theses

• P. Scheiblechner: On the Complexity of Counting Irreducible Components and Computing Betti Numbers of Algebraic Varieties, PhD Thesis (2007). Advisor: Prof. Peter Bürgisser.
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• P. Scheiblechner: Eine C++-Bibliothek für verschiedene algebraische Strukturen, Diploma Thesis (1997). Advisor: Prof. Christian Bär.
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Upcoming Events

Past Events

• Forschungssymposium Gesundheit Luzern 2025, Lucerne, Switzerland, January 29, 2025.
• Forschungssymposium Gesundheit Luzern 2024, Lucerne, Switzerland, January 31, 2024.
• The 4th Swiss Conference on Data Science - SDS|2017, Bern, Switzerland, June 16, 2017.
• The 3rd Swiss Conference on Data Science - SDS|2016 and SDS Deep Learning Day 2016, Winterthur, Switzerland, September 15 - 16, 2016.
• Workshop Real-Number Complexity of Foundations of Computational Mathematics, Montevideo, Uruguay, December 11 - 20, 2014.
• Dagstuhl Seminar: Computational Counting, Dagstuhl, Germany, January 13 - 18, 2013.
• 64. Theorietag - Workshop über Algorithmen und Komplexität, Darmstadt, Germany, October 4-5, 2012.
• ISSAC 2012, 37th International Symposium on Symbolic and Algebraic Computation, Grenoble, France, July 22 - 25, 2012.
• Mini-Symposium on Algebraic Complexity at SIAM Conference on Applied Algebraic Geometry, Raleigh, North Carolina, USA, October 6 - 9, 2011.
• Topical Workshop Mathematical Aspects of P versus NP and its Variants of the Institute for Computational and Experimental Research in Mathematics, Providence, Rhode Island, USA, August 1 - 5, 2011.
• Workshop Real-Number Complexity of Foundations of Computational Mathematics, Budapest, Hungary, July 4 - 14, 2011.
• Dagstuhl Seminar: Computational Counting, Dagstuhl, Germany, November 28 - December 3, 2010.
• Algebra, Geometry, and Combinatorics Day, Urbana Champaign, IL, USA, Oktober 16, 2010.
• Advances in the Theory of Computing 2010, special track of SYNASC 2010, the 12th Annual Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, September 23 - 26, 2010.
• Algebra, Geometry, and Combinatorics Day, West Lafayette, IN, USA, May 1, 2010.
• The Decomposition Theorem and the Topology of Algebraic Maps, Freiburg, Germany, February 22 - 26, 2010.
• Logical Approaches to Barriers in Computing and Complexity, Greifswald, Germany, February 17 - 20, 2010.
• Oberwolfach Seminar: New Trends in Algorithms for Real Algebraic Geometry, Mathematisches Forschungsinstitut Oberwolfach, Germany, November 22 - 28, 2009.
• Workshop on Complexity of Numerical Computation, Thematic Program on the Foundations of Computational Mathematics, Fields Institute, Toronto, Ontario, Canada, October 20 - 24, 2009.
• Algebra, Geometry, and Combinatorics Day, Urbana Champaign, IL, USA, September 26, 2009.
• MEGA 2009, Barcelona, Spain, June 15 - 19, 2009.
• 2nd Bluegrass Algebra Conference 2009, Lexington, KY, USA, March 6 - 8, 2009.
• FoCM 2008, Hong Kong, China, June 16 - 26, 2008.
• ISSAC 2007, Waterloo, Ontario, Canada, July 29 - August 1, 2007.
• FoCM 2005, Santander, Spain, June 30 - July 9, 2005.

Lucerne University of Applied Sciences and Arts
Technology and Architecture
Technikumstr. 21
CH-6048 Horw
Switzerland
Phone: +41 41-349 35 13