Nicholas Pischke

I'm a mathematician and computer scientist working in the field of (mathematical) logic, with a focus on proof theory, pure and applied. In particular, I am interested in Gödel's functional interpretation and its applications in different parts of mathematics and computer science, most recently stochastic approximation and optimization, often combined with metric geometry. In the past, I have also been interested in modal logics, many-valued logics and intermediate logics and the resulting combination thereof as well as structural proof theory.

I am a Lecturer (equivalent to Assistant Professor) in the Department of Computer Science at the University of Bath, and a member of the Mathematical Foundations of Computation Group.

Picture credit: Oberwolfach Photo Collection

Before that, I was a post-doctoral researcher in the Logic Group within the Department of Mathematics at TU Darmstadt. I obtained my PhD (Dr.rer.nat.) from the same department with a thesis written under the supervision of Ulrich Kohlenbach.

Email: pischkenicholas [at] gmail [dot] com / nnp39 [at] bath [dot] ac [dot] uk

A proof mining bibliography: alphabetical and chronological

Notes and Papers

Preprints

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
submitted, 24pp. (ArXiv, PDF)
On the asymptotic behaviour of stochastic processes, with applications to supermartingale convergence, Dvoretzky's approximation theorem, and stochastic quasi-Fejér monotonicity
with Morenikeji Neri and Thomas Powell, submitted, 40pp. (ArXiv, PDF)
Asymptotic regularity of a generalised stochastic Halpern scheme
with Thomas Powell, submitted, 33pp. (ArXiv, PDF)
A proof-theoretic bound extraction theorem for monotone operators in Banach spaces
submitted, 38pp. (PDF)
On Dykstra's algorithm with Bregman projections
with Pedro Pinto, submitted, 23pp. (Oberwolfach Preprint, PDF)

Publications

On the Halpern method with adaptive anchoring parameters
with Pedro Pinto, to appear in: Mathematics of Computation (2025+), 23pp. (Oberwolfach Preprint, PDF, doi)
Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions
with Ulrich Kohlenbach, to appear in: Computational Optimization and Applications (2025+), 33pp. (PDF, doi)
On the proximal point algorithm for strongly quasiconvex functions in Hadamard spaces
to appear in: Optimization Methods and Software (2025+), 14pp. (ArXiv, PDF, doi)
Duality, Fréchet differentiability and Bregman distances in hyperbolic spaces
to appear in: Israel Journal of Mathematics (2025+), 40pp. (PDF)
Proof mining and probability theory
with Morenikeji Neri, Forum of Mathematics, Sigma 13 (2025), e187, 47pp. (ArXiv, PDF, doi)
Generalized Fejér monotone sequences and their finitary content
Optimization 74(14) (2025), pp. 3771-3838 (ArXiv, PDF, doi)
On logical aspects of extensionality and continuity for set-valued operators with applications to nonlinear analysis
Mathematical Structures in Computer Science 35 (2025), e15, 27pp. (PDF, doi)
Generalized learnability of stochastic principles
with Morenikeji Neri and Thomas Powell, Proceedings of the 21st Conference on Computability in Europe, A. Beckmann, I. Oitavem, F. Manea (eds), LNCS 15764, Springer (2025), pp. 333-348 (PDF, doi)
A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications
Selecta Mathematica 31(2) (2025), 32, 67pp. (ArXiv, PDF, doi)
Effective rates for iterations involving Bregman strongly nonexpansive operators
with Ulrich Kohlenbach, Set-Valued and Variational Analysis 32(4) (2024), 33, 58pp. (PDF, doi)
Proof mining for the dual of a Banach space with extensions for uniformly Fréchet differentiable functions
Transactions of the American Mathematical Society 377(10) (2024), pp. 7475-7517 (PDF, doi)
Rates of convergence for the asymptotic behavior of second-order Cauchy problems
Journal of Mathematical Analysis and Applications 533(2) (2024), 128078, 15pp. (ArXiv, PDF, doi)
Logical Metatheorems for Accretive and (Generalized) Monotone Set-Valued Operators
Journal of Mathematical Logic 24(2) (2024), 2350008, 59pp. (ArXiv, PDF, doi)
On Computational Properties of Cauchy Problems generated by Accretive Operators
with Pedro Pinto, Documenta Mathematica 28(5) (2023), pp. 1235-1274 (ArXiv, PDF, doi)
On Korpelevich's Extragradient Algorithm
Zeitschrift für Analysis und ihre Anwendungen 42(1/2) (2023), pp. 117-129 (PDF, doi)
Proof Theory and Nonsmooth Analysis
with Ulrich Kohlenbach, Philosophical Transactions of the Royal Society A 381(2248) (2023), 20220015, 21pp. (PDF, doi)
Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space
Journal of Convex Analysis 30(1) (2023), pp. 295-315 (ArXiv, PDF, link)
On Infinitary Gödel Logics
Journal of Logic and Computation 33(1) (2023), pp. 1-46 (ArXiv, PDF, doi)
On Intermediate Justification Logics
Logic Journal of the IGPL 31(1) (2023), pp. 534-573 (ArXiv, PDF, doi)
Quantitative Analysis of a Subgradient-Type Method for Equilibrium Problems
with Ulrich Kohlenbach, Numerical Algorithms 90(1) (2022), pp. 197-219 (ArXiv, PDF, doi)
Gödel Justification Logics and Realization
Logic Journal of the IGPL 30(3) (2022), pp. 343-408 (ArXiv, PDF, doi)
A Note on Strong Axiomatization of Gödel Justification Logic
Studia Logica 108(4) (2020), pp. 687-724 (ArXiv, PDF, doi)

Abstracts

Proof mining and probability theory
Abstract in 2024 European Summer Meeting of the Association for Symbolic Logic: Logic Colloquium 2024.
Bulletin of Symbolic Logic 30(4) (2024), p. 613. (doi)
Proof-Theoretical Aspects of Nonlinear and Set-Valued Analysis
Bulletin of Symbolic Logic 30(2) (2024), pp. 288-289. (doi)
Intensional methods in applied proof theory
Abstract in 2023 European Summer Meeting of the Association for Symbolic Logic: Logic Colloquium 2023.
Bulletin of Symbolic Logic 30(1) (2024), p. 101. (doi)
Proof Mining and duality in Banach spaces
Abstract in S. Buss, R. Iemhoff, U. Kohlenbach, M. Rathjen: Mathematical Logic: Proof Theory, Constructive Mathematics.
Oberwolfach Reports 20(4) (2023), p. 3030. (doi or doi)
Quantitative results for equilibrium problems
Abstract in S. Buss, R. Iemhoff, U. Kohlenbach, M. Rathjen: Mathematical Logic: Proof Theory, Constructive Mathematics.
Oberwolfach Reports 17(4) (2020), pp. 1737-1738. (doi or doi)

Notes

A Subset Semantics for the Weak Gödel Modal Logics (PDF)
On Decidability and Complexity of Gödel Justification Logic (PDF)
A note on Public Announcements in Standard Gödel Modal Logic (ArXiv, PDF)
Dynamic extensions for the logic of knowing why with public announcements of formulas (ArXiv, PDF)

Note that the PDF link provides you with a newer version than the ArXiv link.

Talks

Upcoming Talks

TBA
Logic Colloquium 2026, Invited Plenary Talk, Swansea University
June 29 - July 3, 2026.

Past Talks

Recent progress in proof mining and probability theory
International Workshop on Programs from Proofs, University of Bath
September 15 - September 16, 2025.
Generalizations through proof mining: A potential for automated reasoning?
Programs from proofs meets formal mathematics, Workshop at ESSLLI 2025, Ruhr-Universität Bochum
July 28 – August 1, 2025.
Proof-Theoretical Aspects of Nonlinear and Set-Valued Analysis
Colloquium Logicum 2024, PhD Colloquium (invited), Österreichische Akademie der Wissenschaften
October 7 - October 9, 2024.
New horizons in (quantitative) Fejér monotonicity
Workshop on Proof Mining 2024, Technische Universität Darmstadt
September 4 - September 6, 2024.
Duality, Fréchet Differentiability and Bregman Distances in Hyperbolic Space
Proof Mining Seminar, LOS-ILDS, Universitatea din București (online)
March 20, 2024.
Generalized Fejér Monotone Sequences
Proof Mining Seminar, LOS-ILDS, Universitatea din București (online)
March 13, 2024.
Proof-theoretically tame approaches to some tameless areas of mathematics
Oberseminar "Mathematische Logik", Julius-Maximilians-Universität Würzburg
November 20, 2023.
Proof Mining and duality in Banach spaces
Oberwolfach Workshop "Mathematical Logic: Proof Theory, Constructive Mathematics"
November 12 - November 17, 2023.
Intensional Methods in Applied Proof Theory
Logic Colloquium 2023, Special Session on Applied Proof Theory (invited), Università degli Studi di Milano
June 5 - June 9, 2023.
Proof mining for the dual of a Banach space and extensions
Seminário de Lógica Matemática, Faculdade de Ciências, Universidade de Lisboa (online)
March 17, 2023.
A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications
Proof Mining Seminar, LOS-ILDS, Universitatea din București (online)
January 11, 2023.
Proof Mining and Monotone Operator Theory
International Conference on Applied Proof Theory, Università degli Studi "G. d'Annunzio" Chieti - Pescara
August 29 - September 2, 2022.
Proof mining for maximally monotone set-valued operators
Proof Mining Seminar, LOS-ILDS, Universitatea din București (online)
June 29, 2022.
Bound extraction theorems for proofs involving monotone operators
Seminário de Lógica Matemática, Faculdade de Ciências, Universidade de Lisboa (online)
February 14, 2022.
Quantitative results for differences of maximal monotone operators
Workshop on "New Frontiers in Proofs and Computation", IASM Hangzhou / BIRS (online)
September 12 - September 17, 2021.
Quantitative results for equilibrium problems
Oberwolfach Workshop "Mathematical Logic: Proof Theory, Constructive Mathematics"
November 8 - November 14, 2020.

Events

Upcoming Events

Second Workshop on Proof Mining (WPM26), with Thomas Powell
University of Bath, United Kingdom
September 7 – September 9, 2026

Past Events

Programs from proofs meets formal mathematics, with Thomas Powell
Workshop at ESSLLI 2025, Ruhr-Universität Bochum, Germany
July 28 – August 1, 2025
Workshop on Proof Mining (WPM24), with Ulrich Kohlenbach and Pedro Pinto
Technische Universität Darmstadt, Germany
September 4 – September 6, 2024 (Picture)

Contact

Email: pischkenicholas [at] gmail [dot] com / nnp39 [at] bath [dot] ac [dot] uk

Address:
Wessex House 9.06
Department of Computer Science
University of Bath
Bath BA2 7AY
United Kingdom