I'm a Ph.D. candidate in Western New York, originally from Istanbul. I identify as an interdisciplinary computational mathematician (also he/him) and my study utilizes complex networks, dynamical systems, computational neuroscience and topological data analysis. In particular, I'm interested in both theoretical model-driven analysis of nonlinear systems and data-driven study of natural phenomenon. Subsequently, I foresee my PhD thesis will help me bridge neuro-related applications and math-related inspiration between domains.

I'm co-advised by Sarah Muldoon and Dane Taylor at University at Buffalo, State University of New York (SUNY). My work overlaps with their common research interests.

In my free time, I like exploring outdoors-- hopping around parks, backpacking, foraging mushrooms and trying to find a rock to boulder.

Announcements:
  • I will be organizing a Directed Reading Program (DRP-Turkey) this summer with Eda Kırımlı, Feride Ceren Köse, and Şefika Kuzgun. If you wish to participate and be a mentor or a mentee, feel free to get in touch!


  • Bengier Ülgen Kılıç

    bengieru@buffalo.edu

    Department of Mathematics
    University at Buffalo, SUNY
    244 Mathematics Building
    Buffalo, NY, 14260-2900
    USA

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    Research

    Big data problems necessitate thinking of both imperfect and noisy nature of the real-world as well as complete and efficient nature of the theoretical study. In my work, I bridge two ends and think some data-related problems in the context of abstract simplicial complexes, hypergraphs and multilayer networks, of which we can compute particular properties, and try to develop the mathematical machinery in the interface of topological data analysis (TDA) and network-data analytics to tackle the problem.

    So, as an inspired computational mathematician, my work falls under two complementary classes in which the former examines empirical data that is guided by the domain-expertise with neuroscience and the latter studies synthetic data generated by the neuron models and is guided by the bifurcation theory for dynamics:

  • Applications in computational neuroscience: data-driven modeling of temporal networks, dynamic community detection, neuronal avalanches, topological bio-image segmentation
  • Applications in structure & dynamics interplay: higher-order networks and dynamics, beyond-pairwise signal propagation, topological and geometrical data analyses

  • For a detailed discussion of these topics, please reach out to me for my research statement.

    Publications
  • Bengier Ulgen Kilic and Dane Taylor. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes. arXiv preprint, arXiv:2201.02071, 2022.

  • I have given several contributed talks and presented posters in major conferences on complex networks, dynamical systems and neuroscience.

    Talks
  • Northeastern Regional Conference on Complex Systems (NERCCS), 2022. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes.
  • Northeastern Regional Conference on Complex Systems (NERCCS), 2021. Characterization of communities in dynamic functional networks.
  • Northeastern Regional Conference on Complex Systems (NERCCS), 2021. Geometrical and topological data analyses reveal that higher-order flow structures provide flow channels for neuronal avalanches.
  • Networks2021, A joint Sunbelt and NetSci Conference, 2021. Higher-order flow channels of neuronal avalanches uncovered by topological data analysis of simplicial contagions.

  • Posters
  • Northeastern Regional Conference on Complex Systems (NERCCS), 2022. Skeleton coupling: a novel topologically based method for defining interlayer links in dynamic community detection.
  • Dynamics Days (DD), 2022. Cascades over simplicial complexes preferably follow geometrically reinforced channels.
  • Society for Neuroscience (SFN), 2019. Cell detection and segmentation via persistent homology.
  • Teaching

    One of the duties of my Ph.D. appointment is teaching/TAing the courses in the university. I have taught several key STEM courses in undergraduate math curriculum. Additionally, I worked with undergraduate students on selected topics in computational mathematics.

    University at Buffalo, SUNY
    • Graduate Teaching Assistant, MTH141, College Calculus I, Fall'18
    • Graduate Teaching Assistant, MTH142, College Calculus II, Spring'18/Spring'21
    • Graduate Teaching Assistant, MTH241, College Calculus III, Fall'19/Fall'21/Spring'22
    • Graduate Teaching Assistant, MTH309, Linear Algebra, Spring'20
    • Graduate Teaching Assistant, MTH417, Survey of Multivariable Calculus, Spring'22
    Directed Reading Program (DRP-Turkey)
    • Mentor for the project: Graph theoretical analysis of brain networks , Summer'21
    Directed Reading Program (DRP-UB)
    • Mentor for the project: Network analysis for real-world applications, Spring'22

    Code

    I write modular, well-documented code in Python. Here are some example libraries I developed.

    Neuronal Cascades
      Neuronal Cascades
    • Neuronal Cascades is a python package to run an SI model on a custom-made geometric network and apply TDA (by computing persistent homology(PH)) on the distance matrices obtained by the contagion which recovers the manifold structure of the network.
    Temporal Network Analysis
       Temporal Networks
    • Temporal Network Analysis is a python wrap-up for applying several dynamic community detection methods to time series data. Available options so far are Multilayer Modularity Maximization, Infomap, Tensor Factorization Approach and Dynamic Stochastic Block Model. Package also contains some helper functions for nice rendering of the communities across time.
    DONU-TDA: Donut-like Object segmeNtation Utilizing Topological Data Analysis
       DONUTDA
    • DONUTDA is another python package I coded for applying TDA to biomedical image segmentation. Algorithm takes grayscale images as input and builds cubical complexes. Applying PH yields either connected components or loops in the images. Accordingly, algorithm is suitable for localization/segmentation of different cell types, blob-like or donut-like. For the application oriented faculty and researchers, a graphical user interface is available.