Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The ‘p-adic Stark conjecture at s = 1’ relates the leading terms at s = 1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to E/F . We prove this conjecture unconditionally when E/Q is abelian. Moreover, we also show that for certain non-abelian extensions E/F the p-adic Stark ...

9:30 10:30 Bruce Reed How many edges force an H-minor? 10:30 11:00 Coffee Break 11:00 11:20 Chun-Hung Liu Well-quasi-ordering graphs by the topological minor relation 11:25 11:45 Jean-Florent Raymond An edge variant of Erdős-Pósa property 11:50 12:10 Irene Muzi Subdivisions in 4-connected graphs of large tree-width 12:10 3:30 Lunch and discussion 3:30 4:30 Dan Kral FO limits of trees 4:30 5:00 ...

A sentence σ ∈ L ω1,ω is a counterexample to Vaught's Conjecture, or simply a counterexample, if ℵ 0 < I(σ, ℵ 0) < 2 ℵ0 , i.e., σ has uncountably many countable models but fewer than continuum many models. Fix σ a counterexample. A key fact about counterexamples is that there are few types for any count-able fragment. Let F be a fragment. Let

We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banach spaces.

It is proved that over every countable field K there is a nil algebra R such that the algebra obtained from R by extending the field K contains noncommutative free subalgebras of arbitrarily high rank. It is also shown that over every countable field K there is an algebra R without noncommutative free subalgebras of rank two such that the algebra obtained from R by extending the field K contain...

In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool in our method is the derivation of a new identity which we call the generaliz...

This is a survey of recent advances on zero-sum problems and Snevily’s conjecture concerning finite abelian groups. In particular, we will introduce Reiher’s recent solution to the Kemnitz conjecture and our simplification. 1. On Zero-sum Problems The theory of zero-sums began with the following celebrated theorem. The Erdős-Ginzburg-Ziv Theorem [Bull. Research Council. Israel, 1961]. For any c...

This is the part II of our series of two papers, “Clemens conjecture: part I”, “Clemens conjecture: part II”. Continuing from part I, in this paper we turn our attention to general quintic threefolds. In some universal quintic threefold X, we construct a family of quasi-regular deformations Bb such that the generic member in this family is non-deviated, but some special member is deviated. By t...

Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...

we investigate the classical h.~zassenhaus conjecture‎ ‎for integral group rings of alternating groups $a_9$ and $a_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎as a consequence of our‎ ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.