Caner Koca

Associate Professor of Mathematics
City University of New York (CUNY)
New York City College of Technology

Research | Teaching

CUNY Kähler Geometry Workshop
January 19-20, 2019

Dr. Caner Koca

I am an Associate Professor at the City University of New York (CUNY) - NYC College of Technology, Department of Mathematics.

I received my Ph.D. from Stony Brook University, Department of Mathematics. My advisor is Claude LeBrun. I am studying Complex Differential Geometry, in particular Kaehler, Einstein and extremal metrics on complex surfaces. Also, I am interested in Algebraic Geometry, especially in the moduli spaces of K3-quotients.

After receiving my PhD, I worked at Vanderbilt University, Department of Mathematics as a post-doctoral assistant professor from 2012 to 2015.

Research Teaching Contact

Research

Current research interests

(1) Kahler geometry, extremal Kahler metrics, Kahler-Einstein metrics, Einstein-Maxwell Metrics
(2) the geometry and moduli spaces of K3 and Enriques surfaces, and various lattice-theoretical problems arising from their middle dimensional cohomology.

Research Grants

  • PSC-CUNY Enhanced Grant (2018-2019). Co-PI: Mehdi Lejmi
  • PSC CUNY A Grant (2016-2017),

Publications

  1. Hermitian Metrics of Constant Chern Scalar Curvature on Ruled Surfaces, co-author: Mehdi Lejmi, Kodai Mathematical Journal, Volume 43, Issue 3, (2020), 409-430.

  2. Einstein-Maxwell Equations on 4-Dimensional Lie Algebras, co-author: Mehdi Lejmi, Canadian Mathematical Bulletin, Volume 62, Issue 4, (2019), 822-840.

  3. On the Curvature of Einstein-Hermitian Surfaces, co-author: M. Kalafat, Illinois J. Math., Volume 62, Number 1-4, (2018), 25-39.

  4. Strongly Hermitian Einstein-Maxwell Solutions on Ruled Surfaces, co-author: Christina Tonnesen-Friedman, Annals of Global Analysis and Geometry, Volume 50, Issue 1, (2016), 29-46.

  5. Complex Surfaces of Locally Conformally Flat Type, co-author: M. Kalafat, Houston J. Math, Volume 42, Issue 4, (2016), 1127-1139.

  6. Conformally Kaehler surfaces and orthogonal holomorphic bisectional curvature, co-author: M. Kalafat, Geometriae Dedicata 174, Issue 1, (2015), 401-408.

  7. Einstein Hermitian Metrics of Positive Sectional Curvature, Proc. of Am. Math. Soc. 142 (2014), 2119-2122.

  8. Extremal Kaehler Metrics and Bach-Merkulov Equations, J. Geom. Phys. 70 (2013), 117-122.

  9. Irreducible Heegner divisors in the period space of Enriques surfaces, co-author: Sinan Sertöz, Int. J. Math., Vol.19, No.2 (2008) , 209-215.

  10. Poincare-Einstein Metrics on Some Ruled Surfaces, in preparation.

  11. On Conformal Geometry of Kahler Surfaces, PhD Thesis, Stony Brook, 2012.

  12. Orbits in the anti-invariant sublattice of the K3-lattice, Master’s Thesis, Bilkent, 2005.

PhD Thesis

On Conformal Geometry of Kahler Surfaces, advisor: Claude LeBrun, Stony Brook University, Department of Mathematics, 2012.

Master's Thesis

Orbits in the anti-invariant sublattice of the K3-lattice, supervisor: Sinan Sertöz, Bilkent University, Department of Mathematics, Ankara/Turkey, 2005. The text is available at Bilkent Univesity Thesis Database, #0002870.

Some of my expository notes:

  1. Notes on Morrison's paper "On K3 surfaces with large Picard number", 2005. [pdf]
    Content: This is a shorth review note on David Morrison's paper "On K3 Surfaces with large Picard number", Invent. Math. 35, 105-121, 1984. A couple of new results and applications are also given in the exposition.

Teaching

Current teaching (Spring 2022)

MAT 2440
Discrete Mathematics 1
MAT 2680
Differential Equations

MAT 2540: Discrete Mathematics II (Spring 2017)

Click to view the links for codes, projects, syllabus, and schedule

The following algorithms are coded in class. All programs are written in C++.

  1. Finding Maximum for a given list of integers cpp.sh link

  2. Finding Maximum for a given list of integers (interactive version) cpp.sh link

  3. Finding the location of the last even integer for a given list of integers cpp.sh link

  4. Linear Search Algorithm cpp.sh link

  5. BubbleSort Algorithm cpp.sh link

  6. Conference Scheduling (Greedy Algorithm) cpp.sh link

  7. Prime Number Check (extremely slow, O(n) complexity) cpp.sh link

  8. Prime Number Check (relatively fast, O(sqrt n) complexity) cpp.sh link

  9. A simple example with pointers cpp.sh link

  10. Binary Search Tree cpp.sh link

  11. Family Tree example for Project 2 cpp.sh link | Alternate Link


Projects:

  1. Finding Minimum. Implementing Selection Sort [pdf]

  2. Implementing Family Trees. Determining family relations [pdf]

Course Information:

  1. Syllabus [4pm course pdf] [6pm course pdf]

  2. Schedule [pdf]

  3. Piazza: Online discussion board for MAT 2540 [link]

Past teaching

City University of New York

Spring 2022:
  • MAT 2440 Discrete Structures and Algorithms I.
  • MAT 2680 Differential Equations.
Fall 2021:
  • MAT 1575 Calculus II.
  • MAT 2630 Numerical Analysis.
Spring 2021:
  • MAT 2540 Discrete Structures and Algorithms II.
  • MAT 2680 Differential Equations.
Fall 2020:
  • MAT 1475 Calculus I.
  • MAT 2540 Discrete Structures and Algorithms II.
Spring 2020:
  • MAT 2540 Discrete Structures and Algorithms II.
  • MAT 2630 Numerical Analysis.
Fall 2019:
  • MAT 1375 Precalculus.
  • MAT 1575 Calculus II.
Spring 2018:
  • MAT 4788 Financial Risk Analysis .
  • MAT 1575 Calculus II.
Fall 2017:
  • MAT 3788 Applications of Heat Equation in Mathematical Finance (Black-Scholes Equation) .
  • MAT 2675 Calculus III: Multivariable Calculus.
Summer 2017:
  • MAT 2440 Discrete Mathematics I. .
  • MAT 1575 Calculus II.
Spring 2017:
  • MAT 2540 Discrete Structures and Algorithms II .
Fall 2016:
  • MAT 2540 Discrete Structures and Algorithms II .
  • MAT 1575 Calculus II.
Spring 2016:
  • MAT 2540 Discrete Structures and Algorithms II .
  • MAT 2675 Calculus III.
Fall 2015:
  • MAT 2675 Calculus III.
  • MAT 2680 Differential Equations.

Vanderbilt University

Summer 2015:
  • MAT 155A Accelerated Single-Variable Calculus I.
Spring 2015:
  • MAT 261 Complex Variables.
Fall 2014:
  • MAT 155A Accelerated Single-Variable Calculus I.
Spring 2014:
  • MAT 155B Accelerated Single-Variable Calculus II.
Fall 2013:
  • MAT 155A Accelerated Single-Variable Calculus I.
Spring 2013:
  • MAT 175 Multivariable Calculus.
Fall 2012:
  • MAT 150A Single-Variable Calculus I.
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Stony Brook University

Spring 2007:
Fall 2006:
Summer-II 2006:
Spring 2006:
Fall 2005:
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Contact Information

Address: CUNY-NYC College of Technology, Department of Mathematics, 300 Jay St., Brooklyn, NY 11201.

718-260-5380