Related papers: The Theorem of Kronheimer-Mrowka

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…

We investigate Seiberg-Witten theory in the presence of real structures. Certain conditions are obtained so that integer valued real Seiberg-Witten invariants can be defined. In general we study properties of the real Seiberg-Witten…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

We present a framework for studying transverse knots and symplectic surfaces utilizing the Seiberg-Witten monopole equation. Our primary approach involves investigating an equivariant Seiberg-Witten theory introduced by Baraglia-Hekmati on…

We study the Seiberg-Witten invariant $\lambda_{\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1\times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an…

We prove a variation of Gronwall's lemma.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

In this note, we present a proof of Donaldson's Diagonalization Theorem via an abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple spinors. Like the other proof of Donaldson's theorem using the standard…

We give a short proof for the fact that rationality of complex surfaces is a property depending only on the differential structure. Our proof uses the new Seiberg-Witten invariants.

The volume conjecture, formulated recently by H. Murakami and J. Murakami, is proved for the case of torus knots.

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We consider the construction of refined Chern-Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then…

We prove a Thom isomorphism theorem for differential forms in the setting of transverse Lie algebra actions on foliated manifolds and foliated vector bundles.

This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.

We show the "non-existence" results are essential for all the previous known applications of the Bauer-Furuta stable homotopy Seiberg-Witten invariants. As an example, we present a unified proof of the adjunction inequalities. We also show…

The paper presents a counterexample to the Hodge conjecture.

We generalize the notion of Thom polynomials from singularities of maps between two complex manifolds to invariant cones in representations, and collections of vector bundles. We prove that the generalized Thom polynomials, expanded in the…