Date: Wed. **November 22, 2023**

Event: FAU MoD Lecture Series (Special double session. November 2023)

Event type: On-site / online

Organized by: FAU MoD, the FAU Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

First session: **13:45H**

**FAU MoD Lecture: Prospects of formalized mathematics**

Speaker: Prof. Dr. **Michael Kohlhase**

Affiliation: Friedrich-Alexander-Universität Erlangen-Nürnberg

**Abstract. ** In (informal) mathematics (pure and applied) a human studies rigorously represented objects or mathematical models of the real world, comes up with conjectures about their properties, proves or refutes them, submits them for review and finally publication in the academic literature.

While it is commonly accepted that all of mathematics could be expressed and indeed developed in first-order logic based on (some axiomatic) set theory, this option is almost never executed in practice.

Formalized mathematics aims to enable computer support of “doing mathematics” by representing objects, conjectures, proofs, and even publications in formal systems, usually expressive logical languages with machine-checkable proof calculi, and highly efficient algorithms for automating various aspects of “doing mathematics”.

Highlights of formalized mathematics are

– machine-checked proofs of major theorems like the Kepler Conjecture,

– Feit/Thomson’s “odd order theorem”, or the four color theorem,

– search engines for mathematical formulae,

– synthesis and verification of computer algebra algorithms

– multiple libraries of formalized and verified mathematics

with more than 100.000 theorems/proofs each.

This talk will give an overview over the issues and results and introduces some of the techniques.

Second session: **15:00H**

**FAU MoD Lecture: Rigorous analysis and numerical implementation of nudging data assimilation algorithms**

Speaker: Prof. Dr. **Edriss S. Titi**

Affiliation: University of Cambridge. Texas A&M University. Weizmann Institute of Science

**Abstract. ** In this talk, I will introduce downscaling data assimilation algorithms for weather and climate prediction based on discrete coarse spatial scale measurements of the state variables (or only part of them, depending on the underlying model). The algorithm is based on linear nudging of the coarse spatial scales in the algorithm’s solution toward the observed measurements of the coarse spatial scales of the unknown reference solution. The algorithm’s solution can be initialized arbitrarily and is shown to converge at an exponential rate toward the exact unknown reference solution. This indicates that the dynamics of the algorithm is globally stable (not chaotic) unlike the dynamics of the model that governs the unknown reference solution. Capitalizing on this fact, I will also demonstrate uniform in time error estimates of the numerical discretization of these algorithms, which makes them reliable upon implementation computationally. Furthermore, I will also present a recent improvement of this algorithm by employing nonlinear nudging, which yields a super exponential convergence rate toward the unknown exact reference solution.

##### Our speakers

**Michael Kohlhase** member at our FAU MoD is professor for Knowledge Representation/Processing (Computer Science) at Friedrich-Alexander-Universität Erlangen-Nürnberg and adjunct associate professor for Computer Science at Carnegie Mellon University.

His research interests include knowledge representation for STEM (Science, Technology, Engineering, Mathematics), inference-based techniques for natural language processing, computer-supported education and user assitance. He pursues these (interrelated) topics focusing on the aspects of modular foundations (usually logical methods) and large-scale structures in document corpora. The research is conducted in the context of the KWARC group (Knowledge Adaptation and Reasoning for Content) and in extended visits to Carnegie Mellon University, SRI International, and the Universities of Amsterdam, Edinburgh, and Auckland.

**Edriss S. Titi** received his doctorate in 1986 under the supervision of Ciprian Foias. Currently he holds the Nonlinear Mathematical Sciences Professorial Chair at the University of Cambridge, UK; he is a University Distinguished Professor and the Arthur Owen Professor of Mathematics in Texas A&M University; moreover, of Computer Science and Applied Mathematics at the Weizmann Institute of Science in Israel.

Titi’s research in applied and computational mathematics lies at the interface between rigorous applied analysis and physical applications. Specifically, in studying the Euler and the Navier-Stokes and other related nonlinear partial differential equations.

Titi is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics, the John Simon Guggenheim Memorial Foundation, USA; and the Institute of Physics, UK. He is also the recipient of many international scientific awards including the Humboldt Research Award and the Einstein Visiting Fellow. He is also a co-recipient of the Society for Industrial and Applied Mathematics (SIAM) Prize on Best Paper in Partial Differential Equations (2009), and the 2020 International Consortium of Chinese Mathematicians Best Paper Award (Gold Medal).

##### This event on LinkedIn

##### Recording/Video

##### AUDIENCE

This is a hybrid event (On-site/online) open to: Public, Students, Postdocs, Professors, Faculty, Alumni and the scientific community all around the world.

##### WHEN

Wed. **November 22, 2023**

13:45H to 16:15H (Berlin time)

##### WHERE

On-site / Online

[On-site] Room**H16 Hörsaal**

GPS-Koord. Raum: 49.573365N, 11.028918E

Friedrich-Alexander-Universität Erlangen-Nürnberg.

Cauerstraße 7-9, 91058 Erlangen (Germany) [Online] FAU Zoom link

Meeting ID: 624 1094 3213 | 694096

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