Intercity Number Theory Seminar

2006

February 10 Groningen, Room 31 WSN Gebouw (see map)
11:30-12:30 Irene Polo, Cubic surfaces
Abstract. Cubic surfaces are very classical objects in algebraic geometry, studied from the middle of the 19th century onward, starting with work of Cayley and Salmon. Every smooth cubic surface over the complex numbers is isomorphic to the blow-up of the projective plane in six points. We describe an algorithm for finding such an isomorphism, starting from a given cubic with a line on it. We also explain for which cubics over the real numbers, such an isomorphism exists over the real numbers. Many examples will be given.
13:15-14:15 Gert Schneider, A MacWilliams identity for convolutional codes
Abstract. The MacWilliams identity that relates the weight enumerator of a block code to that of a dual code has given rise to numerous applications and an elaborate theory in classical coding theory. For convolutional codes it is known that there is no such relation of the weight distributions of a code and its dual, suggesting that the weight distribution alone does not carry enough information about the code. The weight adjacency matrix associated to a convolutional code is a more refined object, from which the weight distribution can be derived. In this talk I will outline a conjecture of a MacWilliams identity between the weight adjacency matrices of a convolutional code and its dual and sketch the proof of this conjecture for a certain non-trivial class of convolutional codes, that includes block codes and reduces to the ordinary MacWilliams identity in this case.
14:30-15:30 Remke Kloosterman, The L-series of a cubic fourfold
Abstract. Let X be a cubic fourfold. Suppose X contains a surface T that is not a complete intersection. In this case, we call X "special". Over the field of complex numbers, and under certain conditions on the degree of T, Hassett proved that the variety F(X) of lines on X is isomorphic to the desingularized second symmetric product S[2] of a K3-surface S. In this talk we prove a stronger statement: Suppose X and S are as above and S is defined over K, a subfield of the complex numbers. Suppose that S has a K-rational point. Then X has a model over K and F(X) is isomorphic to S[2] over K. In the case S is defined over Q, it has a rational point and the Picard number of S equals 20, we can use the above result to prove that the "interesting" part of the L-function of X equals the L-function of a Hecke eigenform.
15:45-16:45 Jaap Top, Some cubic curves over function fields
Abstract. We discuss the equations y2=x3+tn+1 and y2=x3+xtn+x over the rational function field C(t) over the complex numbers C. Both define elliptic curves, and we compute the rank of the group of C(t)-rational points as a function of n, using a method of T. Shioda. We also discuss how one may find generators of these groups.
February 24 Nijmegen, DIAMANT intercity: Special day on radical extensions
12:10-13:00 Hendrik Lenstra, Algorithmic Galois theory [PDF]
Abstract. Algorithmic Galois theory occupies itself with the design and analysis of efficient algorithms concerning algebraic field extensions. The main purpose of the present lecture is to explain the rules of the game. The best results that have been obtained are related to solvability by radicals, and they have been achieved by means of group theory. A number of open but apparently feasible problems will be formulated.
13:00-14:00 Lunch break
14:00-14:50 Bart de Smit, Entangled radicals [PDF]
Abstract. For a field K of characteristic 0, a radical group is an abelian group B containing K* so that each b in B has a power in K*. If all finite subgroups of B are cyclic, then we can embed B in the multiplicative group of an extension field of K. To analyze the radical field extension K(B) of K one needs to understand relations between radicals, such as √5 + √-5 = 4√-100. We will show that these are controlled by the entanglement group. As an application, we formulate Artin's primitive root conjecture over number fields.
15:00-15:50 Willem Jan Palenstijn, Computing field degrees of radical extensions [PDF]
Abstract. In this talk we will present an algorithm that efficiently computes the field degree of finite radical extensions over the rationals, up to a suitably defined cyclotomic part. The main ingredient is the theory developed in the previous lecture.
15:50-16:10 Tea break
16:10-17:00 Wieb Bosma, Some radical algorithms in Magma
Abstract. We will discuss several problems and examples of representing certain elements in solvable number fields as nested radicals in the computer algebra system Magma. The problems have to do with ambiguities arising from multivalued root extraction, with testing for equality, with simplification, and with finding such a representation.
March 10 Leiden, room 403
11:30-12:30, 13:30-14:30 E. Friedman (U. of Chile), Survey of Lehmer's Conjecture
Abstract. Kronecker showed that if the roots of a polynomial P(x), assumed monic, irreducible and with integer coefficients, all lie on the unit circle in the complex plane, then the roots of P(x) are actually just roots of unity. But how close to the unit circle can the roots of P(x) be without them all actually being on the unit circle? This simple-looking question turns out to be difficult and we have only partial answers. Lehmer suggested in 1933 a surprisingly precise answer which has stood the test of time.
I will describe what is known about Lehmer's conjecture and how it relates to some other aspects of number theory. I will give Smyth's simple 1971 proof solving Lehmer's problem for non palindromic polynomials (a polynomial is palindromic if the sequence of coefficients reads the same backwards or forwards). This result gives the problem additional structure, allowing the introduction of tools from algebraic and analytic number theory.
The exposition is meant to be accessible to Master's program students, with essentially no prerequisites (more truthfully, the first hour will require nothing beyond the Taylor series of an analytic function, the second hour will require an acquaintance with basic elements of algebraic number theory such as discriminants, regulators and absolute values).
14:45-15:30 J. Brakenhoff (Leiden), Squarefree discriminants
Abstract. Let fZ[X] be a monic polynomial of degree n≥2. Denote by Δ(f) the discriminant of f. We want to determine the probability that Δ(f) is squarefree. Looking locally at each prime, we can find a heuristic value for this probability, which depends on n.
15:45-16:45 S. Vostokov (St. Petersburg), Reciprocity laws:yesterday and today
Abstract. In the talk the origins of reciprocity laws from Euler to our time will be discussed. We start with the classical version, then go to Hilbert's interpretation of this law and discuss the current state of the problem and basic results. We also discuss applications of the reciprocity law to other problems in arithmetic.
March 24 Utrecht, Room K11 (basement)
11:30-12:30, 13:30-14:30 E. Friedman (U. of Chile), Lehmer's Conjecture and Relative Regulators
Abstract. Smyth showed in 1971 that if a polynomial (assumed monic, irreducible, with integer coefficients and of degree at least 2) is not palindromic, then its roots cannot be too close to the unit circle, in a certain precise sense. (A polynomial is palindromic if the sequence of coefficients reads the same backwards or forwards.) Lehmer's conjecture states that Smyth's conclusion should hold even for palindromic polynomials, as long as they are not cyclotomic. The simplest open case of Lehmer's conjecture is that of Salem numbers, i.e. of a palindromic polynomial having only one root outside the unit circle. Such a root α is called a Salem number. It is an algebraic unit which generates a number field L=Q(α), endowed with a subfield K=Q(α+α-1) with [L:K]=2 and NormL/K(α)=1. Thus α is a ``relative unit'' of the extension L/K.
I will describe regulators of relative units and a conjectural lower bound for them which would imply the Salem number case of Lehmer's conjecture. I will sketch a proof of this conjecture in the high-rank case. Unfortunately the Salem number case is the rank-one case. I will end by presenting a formula which might pave the way for a proof of the low-rank case. This is joint work with N.-P. Skoruppa, published some 6 years ago, but still unfinished in the low-rank case.
14:45-15:30, 15:45-16:30 F. Beukers (Utrecht), Lower bounds for heights of algebraic points
Abstract. We consider the algebraic points on an algebraic variety defined over the algebraic closure of Q and their absolute normalised logarithmic heights. In many cases it turns out that one can give uniform non-trivial lower bounds for these heights. We start with a remarkable elementary result by Zhang-Zagier and then proceed to discuss some wide generalisations, with applications to diophantine equations.
April 7 Utrecht Room K11 (basement)
11:30-12:20 Marco Streng, Elliptic divisibility sequences with complex multiplication
Abstract. A classical elliptic divisibility sequence (indexed by the integers) arises as denominators of the multiples of a fixed rational point of infinite order on an elliptic curve over the rationals. Such a sequence is knownto have primitive divisors from some point on (as follows from height estimates and Siegel's theorem). If the curve has complex multiplication, we show how the cm-ring can be used to index a similar sequence of ideals and prove that it has primitive divisors. The classical proof breaks down and needs to be replaced by an inclusion/exclusion proof with finer diophantine estimates involving ellipticlogarithms
13:30-14:20 Gunther Cornelissen, Deformations of weakly ramified coverings of curves
Abstract. A cover of curves over a field of characteristicp is said to be weakly ramified if all second ramification groups vanish. I will discuss work with Ariane Mézard that computes the (mixed-characteristic) universal deformation ring of such a cover. Using previous work with Bertin and Kato, one only needs to determine the characteristic of that ring, which turns out to be either p or zero.
14:30-15:20 Jakub Byszewski, A universal deformation ring that is not a complete intersection
Abstract. Bleher and Chinburg recently gave an example of a linear representation of a finite group whose universal deformation ring is not a complete intersection, thus answering a question of Flach. Their proof uses some modular representation theory. We will show that the same result can be proven using only standard cohomological obstruction calculus.
15:40-16:30 Oliver Lorscheid, Toroidal integrals
Abstract. In the 1970's, Don Zagier developed the formalism of toroidal automorphic forms, where the usual parabolic condition is substituted by the vanishing of integrals over various tori. We will outline the relation between these spaces and zeros of zeta functions (via Eisenstein series and Tate's thesis), paying particular attention to the case of a split torus (left somewhat aside in the original work) and to explicit calculation of such integral vanishing conditions in the case of global function fields.
April 21 Groups and characters, a farewell symposium for Rob van der Waall,
Universiteit van Amsterdam, room P.227 of the Euclides building.
See the UvA announcement for directions.
10:30-11:00 Coffee
11:00-11:50 Hendrik Lenstra (Leiden), Factoring polynomials over solvable closures
Abstract. One of Rob van der Waall's most celebrated results concerns solvable extensions of number fields, and it is proved by means of group theory. The same applies to the result that the present lecture is devoted to: there is an efficient algorithm for factoring polynomials over the solvable closure of a number field. Some care is required in formulating precisely what this assertion means, because the solvable closure of any number field is of infinite degree over the field of rational numbers. The lecture will provide the context, the definitions, the algorithm, as well as the result from group theory that is crucial in proving the correctness of the algorithm.
12:00-12:50 Gabriele Nebe (Aachen), Codes and invariant theory
Abstract. In 1970 on the ICM in Nice, A.M. Gleason presented his famous theorem that the weight enumerator of a doubly-even self-dual binary code is an element of the polynomial ring generated by the weight enumerators of the Hamming code of length 8 and the Golay code of length 24. The proof uses the fact that this polynomial ring is the invariant ring of the complex reflection group G9 of order 192. In the meantime, many variations of this theorem have been proven. Together with E. Rains and N. Sloane, we develop a theory that allows us to prove that, in a quite general situation, the weight enumerators of codes of a given Type over a not necessary commutative finite ring span the invariant ring of the associated Clifford-Weil group. These are finite complex matrix groups given by explicit generators.
14:00-18:20 Afternoon program
To attend the afternoon program and the closing reception please register by sending an email to Evelien Wallet at ewallet@science.uva.nl.
This part of the day will include a lecture of Bertram Huppert (Mainz) with the title How to shuffle cards, and lectures by Arjeh Cohen and Rob van der Waall.

Further activities in the summer of 2006

Special day on explicit complex multiplication theory

8 September, Leiden. first lecture: room 403, other three: room 412

It has been known since the 19th century that the values of certain analytic functions, such as the exponential function, generate families of algebraic extensions over the rationals. Despite the exponential nature of the phenomenon, computations in "low genus" are possible, and the genus 1 case is more or less classical. We will review the classical theory from various angles before moving on to computations in genus 2, which are still in their infancy.

12:00–12:45
Peter Stevenhagen, Algebraic extensions from analytic functions
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:45–14:30
Peter Stevenhagen, Explicit computations using Shimura's reciprocity law
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
14:45–15:30
Everett Howe, Complex multiplication of abelian surfaces
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
15:45–16:30
Everett Howe, Explicit computation of Igusa invariants
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.

Intercity Number Theory Seminar

22 September, Utrecht. room K11
11:15–12:00
Frits Beukers, Irrationality of p-adic L-values
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:00–14:00
Vasily Golyshev, Moscow), Spectra and Their Arithmetic
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
14:15–15:15
Jan Stienstra, Apery-like numbers, differential equations of type DN and dimer models
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
15:30–16:15
Sander Dahmen, Lower bounds for numbers of ABC-hits
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.

GTEM Kick-off seminar

13 October, Leiden. Room 312 of the Mathematical Institute (directions)

This is the first seminar of the GTEM Research Training Network.

Michel Matignon, p-Groups and automorphism groups of curves in characteristic p>0
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
René Schoof, Semi-stable abelian varieties and modular curves
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
John Cremona, Lattice reduction over function fields, with applications to finding points on curves over function fields
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
15:00–15:50
Heinrich Matzat, Differential equations and finite groups
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.

Intercity Number Theory Seminar

3 November, Groningen. Room BB217, Blauwborgje 8, Zernike campus (bus 15 from the train station)

11:30–12:30
Andy Pollington, Badly approximable numbers and Littlewood's conjecture in Diophantine approximation
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:00–13:45
Jeroen Sijsling, Dessins d'enfant(s), Platonic or down-to-earth?
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:45–14:30
Lenny Taelman, Permutation groups, linear groups, Galois groups in characteristic p
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
14:45–15:45
Robert Carls, A higher dimensional 3-adic CM construction
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
16:00–17:30
Mohamed Barakat, Homological algebra and applications to linear control theory
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.

DIAMANT intercity seminar on lattices

10 November, Leiden. This day is organized together with Karen Aardal
The first lecture takes place in room C3, the others in room C1 of the Gorlaeus lab (directions).
11:00–12:00
Hendrik Lenstra, A new type of lattices
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:30–14:30
Phong Nguyen, Hermite's constant and lattice reduction algorithms
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
14:45–15:45
Friedrich Eisenbrand, Integer programming: results in fixed dimension
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
16:00–17:00
Karen Aardal, Lattices and integer programming formulations
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.

Special day on Chebotarev and Sato-Tate

24 November, Leiden. Room 412 (first talk), and 312 (others)

Program:

René Schoof, Equidistribution and L-functions
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
13:30–14:30
Gerard van der Geer, Chebotarev for finitely generated fields
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.
14:45–17:00
Bas Edixhoven, Recent results on the Sato-Tate conjecture
In December 2020, Peter Scholze posed a challenge to formally verify the main theorem on liquid ℝ-vector spaces, which is part of his joint work with Dustin Clausen on condensed mathematics. I took up this challenge with a team of mathematicians to verify the theorem in the Lean proof assistant. Half a year later, we reached a major milestone, and our expectation is that shortly we will have completed the full challenge. In this talk I will give a brief motivation for condensed/liquid mathematics, a demonstration of the Lean proof assistant, and discuss our experiences formalizing state-of-the-art research in mathematics.