Related papers: A bijectional attack on the Razumov-Stroganov conj…

We prove the geometric Bogomolov conjecture over a function field of characteristic zero.

We prove the Razumov--Stroganov conjecture relating ground state of the O(1) loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches,…

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

This paper gives a bijective proof of Andrews' refinement of the Alladi-Schur theorem. Moreover, it demonstrates that the bijective framework introduced here can be used to reproduce and provide a bijective account of Andrews' recursive…

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.

We prove Union-Closed sets conjecture.

We provide a proof of Pisot conjecture, a classification problem in Ergodic Theory on recurrent sequences generated by irreducible Pisot substitutions.

These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line,…

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.

The purpose of this proceeding is twofold. Firstly, we shall make the refining of the Gribov-Zwanziger action more complete by taking into account more condensates than considered so far. Secondly, we shall provide more evidence for the…

We propose a conjectural determination of the Gromov-Witten theory of a root stack along a smooth divisor. We verify our conjecture under an additional assumption.

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…

WITHDRAWN: The proof contains an uncorrectable gap in the proof of theorem 7 on page 11. A proof of the Krzyz conjecture is presented, based on the application of the variational method, as well as on the use of two classical results and…

We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…

This is a survey on Sarnak's Conjecture

We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$.…

We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labeled by an arbitrary finite-dimensional representation.…

This paper has been withdrawn by the author due a crucial sign error in Theorem B. We present a geometric proof of Thom conjecture, which uses Khovanov homology. Our approach doesn't use any analytic methods and is quite different from…