Based on an identity of Jacobi, we prove a simple formula that computes the pushforward of
analytic functions of the exceptional divisor of a blowup of a projective variety along a …

We present a simple algebraic construction of all the small resolutions for the SU (5)
Weierstrass model. Each resolution corresponds to a subchamber on the Coulomb branch …

We study the geometry of elliptic fibrations satisfying the conditions of Step 8 of Tate's
algorithm. We call such geometries F $ _4 $-models, as the dual graph of their special fiber …

We consider the 8-supercharge 5d su (N) gauge theories from M-theory compactified on
elliptic Calabi-Yau threefolds. By matching the triple intersection numbers in the elliptic …

We compute characteristic numbers of crepant resolutions of Weierstrass models
corresponding to elliptically fibered fourfolds $ Y $ dual in F-theory to a gauge theory with …

Generalizing the results of 1211.6077 and 1703.00905, we prove a formula for the
pushforward of an arbitrary analytic function of the exceptional divisor class of a weighted …

A Weierstrass fibration is an elliptic fibration $ Y\to B $ whose total space $ Y $ may be given
by a global Weierstrass equation in a $\mathbb {P}^ 2$-bundle over $ B $. In this note, we …

We investigate two different views towards gravitational theories using mathematical
frameworks. First, we study gravitational theories with supersymmetries in various …

In recent years the PI and his students have developed algorithms for finding closed form
solutions of second order linear differential equations with rational function coefficients. The …

The topic in the PI's current grant1 is: Given a linear homogeneous linear differential
equation with polynomial coefficients, decide if it can be solved in terms of special functions …