Nicholas Pischke

I’m a mathematician working in the field of (mathematical) logic, with a focus on proof theory. In particular, I am interested in Gödel's functional interpretation and its applications in the proof mining program. 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 member of 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.

Picture credit: Oberwolfach Photo Collection

Email: pischkenicholas [at] gmail [dot] com / pischke [at] mathematik [dot] tu-darmstadt [dot] de

A proof mining bibliography: alphabetical and chronological

Things of Interest:
The Association for Symbolic Logic has awarded me the Sacks prize for the most outstanding doctoral dissertation in mathematical logic of 2024! You can read about it here. The other winner is Erfan Khaniki who, among many other things, proved the amazing result that not all Kripke models of HA are locally PA!

Notes and Papers

Preprints

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, 41pp. (ArXiv, PDF)

Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions
with Ulrich Kohlenbach, submitted, 24pp. (PDF)

On the proximal point algorithm for strongly quasiconvex functions in Hadamard spaces
submitted, 14pp. (ArXiv, PDF)

Asymptotic regularity of a generalised stochastic Halpern scheme with applications
with Thomas Powell, submitted, 29pp. (ArXiv, PDF)

On the Halpern method with adaptive anchoring parameters
with Pedro Pinto, submitted, 19pp. (Oberwolfach Preprint, 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)

Proof mining and probability theory
with Morenikeji Neri, submitted, 50pp. (ArXiv, PDF)

Publications

On logical aspects of extensionality and continuity for set-valued operators with applications to nonlinear analysis
To appear in: Mathematical Structures in Computer Science (2025+), 28pp. (PDF)

Generalized learnability of stochastic principles
with Morenikeji Neri and Thomas Powell,
To appear in: Proceedings of Computability in Europe 2025, LNCS, Springer (2025+), 15pp. (PDF)

Duality, Fréchet differentiability and Bregman distances in hyperbolic spaces
To appear in: Israel Journal of Mathematics (2025+), 40pp. (PDF)

Generalized Fejér monotone sequences and their finitary content
To appear in: Optimization (2025+), 68pp. (ArXiv, 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-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), pp. 94-139. (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), pp. 3013-3061. (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. 1693-1757. (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.

Events

Upcoming Events

Programs from proofs meets formal mathematics, with Thomas Powell
Workshop at ESSLLI 2025, Ruhr-Universität Bochum, Germany
July 28 – August 1, 2025

Past Events

Workshop on Proof Mining 2024, with Ulrich Kohlenbach and Pedro Pinto
Technische Universität Darmstadt, Germany
September 4 – September 6, 2024