About

Tamal Krishna Dey is a Professor of Computer Science at Purdue University, having joined the department in Fall 2020. His primary research areas include Computational Geometry and Topology, with applications to topological data analysis, geometric modeling, computer graphics, and mesh generation. Dey has authored two books: 'Curve and Surface Reconstruction: Algorithms with Mathematical Analysis' published by Cambridge University Press and 'Delaunay Mesh Generation' published by CRC Press. He recently coauthored another book titled 'Computational Topology for Data Analysis,' scheduled for publication by Cambridge University Press in 2022. With over 200 scientific articles to his name, Dey is an IEEE and ACM Fellow and has been inducted as a Fellow by the Solid Modeling Association. His academic background includes a PhD in Computer Science from Purdue University, a Masters from the Indian Institute of Science, and a Bachelor of Engineering from Jadavpur University. Prior to Purdue, he was a faculty member at Ohio State University from 1999 to 2020, where he led the Jyamiti research group and headed the NSF-sponsored TGDA TRIPODS Phase I Institute. Dey serves on various editorial and executive boards and is a sought-after speaker at academic forums.

Research topics

• Computer science
• Mathematics
• Algorithm
• Combinatorics
• Artificial intelligence

Selected publications

• HalluZig: Hallucination Detection using Zigzag Persistence

  ArXiv.org · 2026-01-04

  articleOpen accessSenior author

  The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate. Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process. In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature. Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.

  PublisherOA PDF

• Limit Computation Over Posets via Minimal Initial Functors

  ArXiv.org · 2026-01-01

  articleOpen access1st authorCorresponding

  It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite poset. We say an initial functor $F\colon C\to D$ with $C$ small is \emph{minimal} if the sets of objects and morphisms of $C$ each have minimum cardinality, among the sources of all initial functors with target $D$. For $Q$ a finite poset or $Q\subseteq \mathbb N^d$ an interval (i.e., a convex, connected subposet), we describe all minimal initial functors $F\colon P\to Q$ and in particular, show that $F$ is always a subposet inclusion. We give efficient algorithms to compute a choice of minimal initial functor. In the case that $Q\subseteq \mathbb N^d$ is an interval, we give asymptotically optimal bounds on $|P|$, the number of relations in $P$ (including identities), in terms of the number $n$ of minima of $Q$: We show that $|P|=Θ(n)$ for $d\leq 3$, and $|P|=Θ(n^2)$ for $d>3$. We apply these results to give new bounds on the cost of computing $\lim G$ for a functor $G \colon Q\to \mathbf{Vec}$ valued in vector spaces. For $Q$ connected, we also give new bounds on the cost of computing the \emph{generalized rank} of $G$ (i.e., the rank of the induced map $\lim G\to \mathop{\mathrm{colim}} G$), which is of interest in topological data analysis.

  PublisherOA PDF

• HalluZig: Hallucination Detection using Zigzag Persistence

  Underline Science Inc. · 2026-03-06

  otherOpen access

  The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate. Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process. In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature. Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and can enable early detection of hallucinations.

  PublisherDOI

• HalluZig: Hallucination Detection using Zigzag Persistence

  2026-01-01

  articleOpen accessSenior author

  The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate.Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process.In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention.We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature.Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures.We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines.Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.

  PublisherOA PDFDOI

• HalluZig: Hallucination Detection using Zigzag Persistence

  arXiv (Cornell University) · 2026-01-04

  preprintOpen accessSenior author

  The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate. Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process. In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature. Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.

  PublisherDOI

• Limit Computation Over Posets via Minimal Initial Functors

  arXiv (Cornell University) · 2026-01-01

  preprintOpen access1st authorCorresponding

  It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite poset. We say an initial functor $F\colon C\to D$ with $C$ small is \emph{minimal} if the sets of objects and morphisms of $C$ each have minimum cardinality, among the sources of all initial functors with target $D$. For $Q$ a finite poset or $Q\subseteq \mathbb N^d$ an interval (i.e., a convex, connected subposet), we describe all minimal initial functors $F\colon P\to Q$ and in particular, show that $F$ is always a subposet inclusion. We give efficient algorithms to compute a choice of minimal initial functor. In the case that $Q\subseteq \mathbb N^d$ is an interval, we give asymptotically optimal bounds on $|P|$, the number of relations in $P$ (including identities), in terms of the number $n$ of minima of $Q$: We show that $|P|=Θ(n)$ for $d\leq 3$, and $|P|=Θ(n^2)$ for $d>3$. We apply these results to give new bounds on the cost of computing $\lim G$ for a functor $G \colon Q\to \mathbf{Vec}$ valued in vector spaces. For $Q$ connected, we also give new bounds on the cost of computing the \emph{generalized rank} of $G$ (i.e., the rank of the induced map $\lim G\to \mathop{\mathrm{colim}} G$), which is of interest in topological data analysis.

  PublisherDOI

• A Fast Algorithm for Computing Zigzag Representatives

  Algorithmica · 2026-04-09

  preprintOpen access1st authorCorresponding

  Abstract Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed in $$O(m^\omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mi>ω</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time, where $$\omega &lt; 2.373$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>2.373</mml:mn> </mml:mrow> </mml:math> is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $$O(m^3)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time, which can be improved to $$O(m^\omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mi>ω</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . However, no known algorithm for zigzag filtrations computes the representatives with the $$O(m^3)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time bound. We present an $$O(m^2n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time algorithm for this problem, where $$n\le m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> is the size of the largest complex in the filtration.

  PublisherDOI

• Computing a Connection Matrix and Persistence Efficiently from a Morse Decomposition

  SIAM Journal on Applied Dynamical Systems · 2026-01-02

  article1st authorCorresponding
  PublisherDOI

• Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data

  ArXiv.org · 2025-02-22

  preprintOpen access1st authorCorresponding

  In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that captures both static and dynamic features at different scales. We present an algorithm to compute this invariant efficiently. We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection, demonstrating its effectiveness in capturing the evolving patterns in time-varying datasets.

  PublisherOA PDFDOI

• A Fast Algorithm for Computing Zigzag Representatives

  Society for Industrial and Applied Mathematics eBooks · 2025-01-01

  book-chapter1st authorCorresponding

  Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. Even though it is known that the barcode for a zigzag filtration with m insertions and deletions can be computed in O (mω) time, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in O (m3) time, which can be improved to O (mω ). However, no known algorithm for zigzag filtrations computes the representatives with the O (m3) time bound. We present an O (m2n ) time algorithm for this problem, where n ≤ m is the size of the largest complex in the filtration.

  PublisherDOI

Recent grants

• AF: Small: Expanding the Reach of Topological Data Analysis

  NSF · $350k · 2020–2024

• MCS: Reconstructing and Inferring Topology and Geometry from Point Cloud Data

  NSF · $462k · 2009–2013

• Collaborative Research: Non-smoothness in Meshing and Reconstruction

  NSF · $429k · 2006–2010

• Inferring Topology and Geometry for Dynamic Shapes

  NSF · $220k · 2008–2011

• AF: Small: Topological Data Analysis for Big and High Dimensional Data

  NSF · $496k · 2013–2018

Frequent coauthors

• Amitava Akuli

  119 shared

• Abhra Pal

  Centre for Development of Advanced Computing

  118 shared

• Nabarun Bhattacharyya

  Symbiosis International University

  115 shared

• Gopinath Bej

  Centre for Development of Advanced Computing

  115 shared

• Sabyasachi Majumdar

  108 shared

• Tapas Sutradhar

  Centre for Development of Advanced Computing

  104 shared

• Rishin Banerjee

  Centre for Development of Advanced Computing

  103 shared

• Moumita Naskar

  100 shared

Education

• PhD, Computer Science

  Purdue University

  1991

Awards & honors

• IEEE Fellow
• ACM Fellow
• Fellow by Solid Modleing Association