# Nancy Abdallah

## PhD in Mathematics

I am a postdoctoral research fellow in the Mathematics department at Linköping University.

## Profile

### Full Name

Nancy Abdallah

### Address

Hus B, rum 2A 649, Campus Valla, Linköping University, Linköping, Sweden

### Born

Lebanon

## Research

### Research Areas

**Algebraic Geometry**

**Algebraic Combinatorics**

**Commutative Algebra**

### Research Topics

**Mixed Hodge Theory of Singular Varieties**

**Plane curves and hyperplane arrangements**

**Syzygies of the Jacobian ideal**

**Coxeter Groups, Kazdhan Lusztig Theory **

### Publications and Preprints

#### N. Abdallah and A. Hultman, Combinatorial Invariance of Kazhdan-Lusztig-Vogan Polynomials for Fixed Point Free Involutions - arxiv:1612.071v1

Abstract. When Sp(2n,C) acts on the flag variety SL(2n,C), the orbits are in bijection with fixed point free involutions in the symmetric group S_2n. In this case, the associated Kazhdan-Lusztig-Vogan polynomials can be indexed by pairs of fixed point free involutions u>u, where > denotes the Bruhat order on the symmetric group. We proved that these polynomials are combinatorial invariants for upper intervals in the Bruhat order on fixed point free involutions.

#### N. Abdallah, On Hodge Theory of Singular Plane Curves - Canad. Math. Bull. 59(2016), 449-460.

Abstract. The dimensions of the graded quotients of the cohomology of a plane curve complement with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration.

#### N. Abdallah, On Plane Curves with Double and Triple Points - Mathematica Scandinavica 119(2016), 60-72.

Abstract. We describe in simple geometric terms the Hodge filtration on the cohomology of the complement of a plane curve with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration.

### Books

#### N. Abdallah, A. Dalmasso, S. Rochow, Fundamental Mathematics for Future Managers - (still in process)

#### N. Abdallah, A. Dalmasso, S. Rochow, Applied Mathematics and Firm Strategy - (still in process)

## Teaching

### 2015

#### Lebanese American University - Lecturer

Fall: Calculus I (Freshman), Biostatistics

#### American University of Beirut - Lecturer

Fall: Calculus I (Freshman)

#### University of Holy Spirit, Kaslik - Lecturer

Fall: Discrete Algebra for Engineering

### 2014 - 2015

#### SKEMA Business School - Instructor

Summer: College Algebra

Fall: Applied Calculus and Matrices, College algebra

#### University of Nice Sophia-Antipolis - Instructor

Fall: Discrete Mathematics for 1st year mathematics for biology (L1SV), 1st year business administration (L1 EG) - Mathematics for economics and 1st year economic and social administration (L1 AES) - Applied Quantitative Techniques

### 2013 - 2014

#### SKEMA Business School - Instructor

Summer, Spring, Fall: College Algebra

#### University of Nice Sophia-Antipolis - Instructor

Spring: 2nd year business administration (L2 EG) - Mathematics for economics

Fall: 2nd year business administration (L2 EG) - Mathematics for economics, 1st year business administration (L1 EG) - Mathematics for economics and 1st year economic and social administration (L1 AES) - Applied Quantitative Techniques

### 2012 - 2013

#### University of Nice Sophia-Antipolis - Instructor

Spring: 2nd year business administration (L2 EG) - Mathematics for economics

Fall: 1st year economic and social administration (L1 AES) - Applied Quantitative techniques

### 2008 - 2010

#### Graduate Assistant at American University of Beirut

### Master Students

#### Jean-Pierre Abi Baroud

## Grants

### 2016 - 2017

Wenner-Gren for a postdoc position at Linkoping University

### 2011 - 2014

CNRS-L for PhD studies at University of Nice

### 2008 - 2010

Scholarship from American University of Beirut for Master Studies

## Education

### 2011 - 2014: Phd in Algebraic Geometry

University of Nice Sophia-Antipolis - Nice - France, Scholarship from CNRS-L