Nicholas Pischke

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.

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, for which I was awarded the Sacks Prize for the most outstanding doctoral dissertation in mathematical logic of 2024 by the Association for Symbolic Logic, among other awards by the TU Darmstadt and the DVMLG.

Picture credit: Oberwolfach Photo Collection

Research Interests: Pure and applied proof theory, Gödel's functional interpretation (and its applications in different parts of mathematics and computer science), non-classical logics (including many-valued and intermediate logics), modal logics, nonlinear analysis, fixed point theory, (stochastic) approximation and optimization, dynamical systems and differential equations, metric geometry.

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

A Proof Mining Bibliography: alphabetical and chronological

Things of Interest:

A recorded lecture of Georg Kreisel on the topic of Herbrand's theorem is available on YouTube, which seems to be the only long form recording of Kreisel available.

Students:

Jacqueline Treusch, PhD student, 2026 - ongoing, University of Bath
Luisa M. Després, Master student, 2025 - 2026, TU Darmstadt (co-supervisor with Ulrich Kohlenbach)

Notes and Papers

Preprints

Strong laws, random monotone vector fields and gradient flows on metric spaces of nonpositive curvature
submitted, 46pp. (ArXiv, PDF)
A relaxed-inertial proximal point algorithm for strongly quasiconvex equilibrium problems on Hadamard manifolds
with Luisa M. Després, submitted, 31pp. (ArXiv, PDF)
On strongly quasiconvex pseudomonotone equilibrium problems in Hadamard spaces
with Luisa M. Després, submitted, 33pp. (ArXiv, PDF)
Weak convergence of the stochastic proximal point method in metric spaces
submitted, 14pp. (ArXiv, PDF)
Avoiding logical strength in real analysis
with Anton Freund and Patrick Uftring, submitted, 60pp. (ArXiv, PDF)
Convergence guarantees for stochastic algorithms solving non-unique problems in metric spaces
with Thomas Powell, submitted, 35pp. (ArXiv, PDF)
An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation
with Morenikeji Neri and Thomas Powell, submitted, 25pp. (ArXiv, PDF)
A systematic way of analysing proofs in probability theory
with Morenikeji Neri and Paulo Oliva, submitted, 50pp. (ArXiv, PDF)
Effective rates for continuous-time quasi-Fejér monotone dynamical systems
with Anton Freund, submitted, 54pp. (ArXiv, PDF)
Generalized fluctuation bounds for stochastic algorithms in the presence of compactness
with Morenikeji Neri and Thomas Powell, submitted, 52pp. (ArXiv, PDF)
On Busemann subgradient methods for stochastic minimization in Hadamard spaces
submitted, 25pp. (ArXiv, PDF)
Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
submitted, 27pp. (ArXiv, 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 (2026+), 25pp. (Oberwolfach Preprint, PDF, doi)
Duality, Fréchet differentiability and Bregman distances in hyperbolic spaces
to appear in: Israel Journal of Mathematics (2026+), 58pp. (PDF, doi)
A proof-theoretic bound extraction theorem for monotone operators in Banach spaces
Monatshefte für Mathematik 211(1) (2026), pp. 107-157 (PDF, doi)
Asymptotic regularity of a generalised stochastic Halpern scheme
with Thomas Powell, Journal of Optimization Theory and Applications 210(1) (2026), Article no. 3, 43pp. (ArXiv, PDF, doi)
Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions
with Ulrich Kohlenbach, Computational Optimization and Applications 93(3) (2026), pp. 1191-1223 (PDF, doi)
On the proximal point algorithm for strongly quasiconvex functions in Hadamard spaces
Optimization Methods and Software 40(6) (2025), pp. 1438-1453 (ArXiv, PDF, doi)
Proof mining and probability theory
with Morenikeji Neri, Forum of Mathematics, Sigma 13 (2025), Article no. 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), Article no. 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), Article no. 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), Article no. 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), Article no. 128078, 15pp. (ArXiv, PDF, doi)
Logical Metatheorems for Accretive and (Generalized) Monotone Set-Valued Operators
Journal of Mathematical Logic 24(2) (2024), Article no. 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), Article no. 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

Effective convergence guarantees for stochastic algorithms in metric spaces
International Symposium on Mathematical Programming 2027, Session on Stochastic Analysis of (Stochastic) Algorithms (invited), Amsterdam
July 25 - July 30, 2027.

Past Talks

Some results in stochastic analysis and optimization over metric spaces of nonpositive curvature
Workshop on Proof Mining 2026, University of Bath
September 7 - September 9, 2026.
Effective convergence guarantees for stochastic algorithms
Mathematisches Kolloquium, Technische Universität Darmstadt
July 15, 2026.
Extracting uniform bounds from proofs in probability theory
Logic Colloquium 2026, Invited Plenary Talk, Swansea University
June 29 - July 3, 2026.
Rates of convergence for a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Proof Mining Seminar, LOS-ILDS, Universitatea din București (online)
April 8, 2026.
An overview of proof mining and probability theory
Seminar of the Theory of Computation Group, University of Birmingham
March 27, 2026.
The computational content of stochastic approximation algorithms
Seminário de Lógica Matemática, Faculdade de Ciências, Universidade de Lisboa (online)
March 16, 2026.
Recent progress in proof mining and probability theory
Oberseminar "Mathematische Logik", Julius-Maximilians-Universität Würzburg
February 9, 2026.
Recent progress in proof mining and probability theory
Seminar of the Centre for Fundamentals of AI and Computational Theory, Queen Mary University of London
January 23, 2026.
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

*cricket noises*

Past Events

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

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