Invited Speakers

Technology Enabled Start-ups (Day 4)

- Manish Gupta, Co-founder, and CEO, VideoKen. Title/Abstract/Bio
- Simon Litsyn, CSO and Co-founder, StoreDot. Title/Abstract/Bio
- Sourish Dasgupta, Co-founder & CEO, Rygbee. Title/Abstract/Bio
- Nirmal Patel, Data Science Lead, Playpower Labs. Title/Abstract/Bio

Graph Theory (Day 5)

- R. Balakrishnan, Bharathidasan University,Tamil Nadu. Title/Abstract/Bio
- T. Karthick, ISI Chennai. Title/Abstract/Bio
- A. Muthusamy, Periyar University,Tamil Nadu. Title/Abstract/Bio
- P. Paulraja, Kalasalingam University, Tamil Nadu. Title/Abstract/Bio
- S. Francis Raj, Pondicherry University, Puducherry. Title/Abstract/Bio
- Shailesh Tipnis, Illinois State University, USA. Title/Abstract/Bio

Title of the talk : Cloud Storage Systems: Latency, Reliability, and Cost

Abstract: Consumers are engaged in more social networking and E-commerce activities these days and are increasingly storing their documents and media in the online storage. Businesses are relying on Big Data analytics for business intelligence and are migrating their traditional IT infrastructure to the cloud. These trends cause the online data storage demand to rise faster than Moore's Law. Erasure coding techniques are used widely for distributed data storage since they provide space-optimal data redundancy to protect against data loss. Cost-effective, network-accessible storage is a strategic infrastructural capability that can serve many businesses. These customers, however, have very diverse requirements of latency, cost, security etc. In this talk, I will describe how to characterize latency. In order to characterize latency, we give and analyze a novel scheduling algorithm. Further, I will present a novel concept of functional caching in storage systems and describe its advantages as compared to duplication in current caching systems. We will validate the results for optimizing a tradeoff between latency and cost using implementations on an open source distributed file system on a public test grid. Finally, I will describe the extensions where the files are video files rather than data files.

Bio: Vaneet Aggarwal received the B.Tech. degree from the Indian Institute of Technology Kanpur, Kanpur, India, in 2005 and the M.A. and Ph.D. degrees from Princeton University, Princeton, NJ, USA, in 2007 and 2010, respectively, all in electrical engineering. He is currently an Assistant Professor in Operations Research at Purdue University and an Adjunct Professor in the Department of Electrical Engineering at IISc Bangalore. He is also affiliated with Computational Science and Engineering Interdisciplinary Program at Purdue. Prior to that, he was a Senior Member of the Technical Staff - Research for about five years with AT&T Labs Research, Bedminster, NJ, USA. Dr. Aggarwal has been an adjunct faculty at Columbia University for two years. His research interests are in the applications of statistical, algebraic, and optimization techniques to communications and networking, distributed computing and storage, and machine learning. Dr. Aggarwal received the Princeton University's Porter Ogden Jacobus Honorific Fellowship in 2009, AT&T Vice President Excellence Award in 2013, and AT&T Senior Vice President Excellence Award in 2014. He also received the 2017 IEEE Jack Neubauer Memorial Award recognizing the best systems paper published in the IEEE Transactions on Vehicular Technology and the 2018 IEEE Infocom Workshop best paper award. Dr. Aggarwal is Senior Member of IEEE, and has been a Program Co Chair for 3rd International Workshop of Software-Defined Data Communications and Storage (SDDCS) 2017. He is serving as an Associate Editor for the IEEE Transactions on Communications and the IEEE Transactions on Green Communications and Networking.

Title of the talk: On the structure and distances of repeated-root constacyclic codes of prime power lengths over finite commutative chain rings.

Abstract: Let p be a prime, s be a positive integer, and let R be a finite commutative chain ring with the characteristic as a power of p. For a unit λ ∈ R, λ-constacyclic codes of length p^s over R are ideals of the quotient ring R[x]/ <x^p^s − λ> . We derive necessary and sufficient conditions under which the quotient ring R[x]/ <x^p^s − λ> is a chain ring. When R[x]/ <x^p^s − λ> is a chain ring, all λ-constacyclic codes of length p s over R are known. We establish algebraic structures of all λ-constacyclic codes of length p s over R when R[x]/ <x^p^s − λ> is a non-chain ring. We also determine the number of codewords in each of these codes. Using their algebraic structures, we obtain symbol-pair distances, Rosenbloom-Tsfasman (RT) distances, and Rosenbloom-Tsfasman (RT) weight distributions of all constacyclic codes of length p s over R. Apart from this, we derive necessary and sufficient conditions under which a constacyclic code of length p^s over R is maximum-distance separable (MDS) with respect to the (i) Hamming metric, (ii) symbol-pair metric, and (iii) Rosenbloom-Tsfasman (RT) met- ric. We also provide an algorithm to decode constacyclic codes of length p^s over R using the known decoding algorithms of linear codes over finite fields with respect to the Hamming, symbol-pair and RT metrics.

Bio: Anuradha Sharma is the Founding Head of the Department of Mathematics at IIIT-Delhi, India. She received B.Sc. degree with Honours in Mathematics, and M.Sc. and Ph. D degrees in Mathematics from Centre for Advanced Study in Mathematics, Punjab University, Chandigarh, India, in 2000, 2002, and 2006, respectively. She was awarded University Gold Medal for standing first in M.Sc. Prior to joining IIIT-Delhi, she has worked as an Assistant Professor in the Department of Mathematics at IIT Delhi for around five and a half years and as an Assistant Professor in the Centre for Advanced Study in Mathematics, Punjab University, Chandigarh for around three years. At IIT Delhi, she received Kusuma Outstanding Young Faculty Fellowship. Currently, she is working in Algebraic Coding Theory. Her other research interests include Number Theory and Algebra. She has over 35 papers in reputed international journals including but not limited to Finite Fields and Applications, Discrete Mathematics, IEEE Transactions on Information Theory, etc. Her Erdos number is 3.

Title of the talk: Graph Energy and Its Related Concepts.

Abstract: Theory of graphs is a branch of discrete mathematics that deals with the way objects are connected. The connectivity in a system is an important characteristic of graph theory. Chemical Graph theory is that branch of mathematical chemistry that is connected with all consequences of connectively in a chemical graph. Such graph serves as a convenient model for any understanding of molecule and reaction scheme in a chemical transformation. Graphs provides simple rule by which chemist may obtain many qualitative prediction about the structure and relatively various compounds. Every chemical molecule can be represented by means of corresponding molecular graphs which represent the constitution of molecule. Each vertex of the graph corresponds to an atom of the molecule. Two vertices are adjacent if there is a bond between the corresponding molecules. The neglects of hydrogen atoms and their bonds cannot be a cause of any ambiguity. In order to simplify the handling of molecular graph, every carbon atom is represented by a vertex and carbon-carbon bond by an edge while hydrogen atoms are ignored. Such graphs are called hydrogen suppressed graphs. The concept of graph energy is one of the frontiers between mathematics and chemistry. It is defined with the help of adjacency matrix of hydrogen suppressed graphs. The energy of graph is sum of the absolute values of eigenvalues of the adjacency matrix. The present talk is intended to give a glimpse of graph energy and its related concepts.

AMS Classification 2010: 05C50, 05C76

Bio: Dr. S. K. Vaidya is presently working as a Professor and head in Department of Mathematics at Saurashtra University, Rajkot, Gujarat, India. He has rich experience of 34 years in mathematical research and teaching. He has supervised about 25 students for M. Phil. and 15 students for Ph. D. Currently, 07 students are in path of obtaining Ph. D. degree under the supervision of Dr. S. K. Vaidya. Till now, he has published about 176 research papers in national as well as international journals. Popularity of his research articles can easily observed by 1093 citations with H-index 17 and i-10 index 43.He is also reviewer of scholarly journals including Discrete Mathematics, Ars Combinatoria, UTILITAS, Journal of Graph Theory and SIAM Journal of Graph Theory etc. He is also a member of editorial board of the journals like Mathematics Today and Journal of Computational Mathematica. He was also conferred by Prof. A. R. Rao encouragement award for research in mathematics for the year 2013. His area of specialization includes graph theory, especially labeling of graphs, domination in graphs and graph energy.

Title of the talk: Applying Machine Learning to Support Human Learning.

Abstract: Rapid changes enabled by technology are making it an imperative for virtually every human being to commit to lifelong learning. The growth of online courses has led to the widespread availability of high quality video lectures on practically any topic. However, much of formal learning, in educational institutions as well as corporations, makes inadequate use of these resources, and purely online learning continues to face challenges that limit its effectiveness. We describe our attempts to improve learning via a platform called VideoKen. Our platform uses novel techniques to support search and recommendation of educational videos on a given topic. VideoKen applies machine learning techniques to index videos, inspired by the analogy with text books, by automatically generating a table of contents and a glossary, and to gain insights from the learner's interactions with the videos. VideoKen also supports social learning at multiple levels. It enables faculty to conveniently share their curated video content within and across institutes, thus helping each other as a community. Likewise, it enables learners also to curate specific video clips and share with their classmates, friends or the organization at large. We describe many outstanding challenges in creating an engaging and personalized learning experience for each learner, and describe our preliminary efforts to deal with those challenges.

Bio: Dr. Manish Gupta is a co-founder and CEO of VideoKen, an educational technology startup, and the Infosys Foundation Chair Professor at IIIT Bangalore. Previously, Manish has served as Vice President and Director of Xerox Research Centre India, and has held various leadership positions with IBM, including that of Director, IBM Research - India and Chief Technologist, IBM India/South Asia. As a Senior Manager at the IBM T.J. Watson Research Center in Yorktown Heights, New York, Manish he led the team developing system software for the Blue Gene/L supercomputer. IBM was awarded a National Medal of Technology and Innovation for Blue Gene by US President Barack Obama in 2009. Manish holds a Ph.D. in Computer Science from the University of Illinois at Urbana Champaign. He has co-authored about 75 papers, with more than 6,000 citations in Google Scholar (and an h-index of 45), and has been granted 19 US patents. While at IBM, Manish received two Outstanding Technical Achievement Awards, an Outstanding Innovation Award, and the Lou Gerstner Team Award for Client Excellence. Manish is an ACM Fellow, a Fellow of the Indian National Academy of Engineering, and a recipient of a Distinguished Alumnus Award from IIT Delhi.

Title of the talk: Recent results on vertex coloring of graphs.

Abstract: Vertex coloring of graphs is one among the well studied topics in the realm of graph theory, and has a long history starting with the four color problem. A proper vertex coloring (or simply coloring) of a graph G is an assignment of colors to the vertices of G such that no two adjacent vertices receive the same color. The minimum number of colors required to color G is called the chromatic number of G, and is denoted by χ(G). The clique number of G, denoted by ω(G), is the maximum size of mutually adjacent vertices in G. Obviously, for any induced subgraph H of G, we have χ(H) ≥ ω(H). A graph G is perfect if every induced subgraph H of G satisfies χ(H) = ω(H). It is well-known that for any integer k ≥ 2, there exists a triangle-free graph with chromatic number equal to k. It follows that for a general class of graphs, there is no upper bound on the chromatic number as a function of its clique number. But for a restricted class of graphs such a function may exist (see [1, 2, 6] and the references therein), and such a function is called a χ-bounding function. For instance, identity function is a χ-bounding function for the class of perfect graphs. In this talk, we show χ-bounding functions for some classes of graphs which do not contain an six vertex induced path, and the talk is based on the papers [3, 4, 5].

References:

[1] Choudum, S. A., Karthick, T., Shalu, M. A.: Perfect coloring and linearly χ-bounded P6-free graphs. Journal of Graph Theory 54(4), 293-306 (2007).

[2] Gyarf ́as, A.: Problems from the world surrounding perfect graphs. Zastosowania Matematyki Applicationes Mathematicae, 19, 413-441 (1987).

[3] Karthick, T., Maffray, F.: Coloring (gem,co-gem)-free graphs. Journal of Graph Theory. Available online.

[4] Karthick, T., Mishra, S.: Chromatic bounds for some classes of 2K2-free graphs. Discrete Mathematics. Accepted for publication.

[5] Karthick, T., Mishra, S.: On the chromati number of (P6, diamond)-free graphs. Graphs and Combinatorics. Available online.

[6] Randerath, B., Schiermeyer, I.: Vertex colouring and forbidden subgraphs - A survey. Graphs and Combinatorics 20, 1-40 (2004).

Bio: Dr T. Karthick is an Assistant professor at ISI Chennai. He completed his M.Sc. and M.Phil. in Mathematics from Bharathidasan University, Tamil Nadu. He holds Ph.D Degree in Mathematics forom IIT Madras under the guidance of Prof. S.A. Choudum. He was at IMSc Chennai and ISI Chennai as Post doc Research Fellow.

Invited Speakers

Coding Theory (Day 1)

Cryptography (Day 2)

Emerging Topics in Discrete Mathematics (Day 3)

Technology Enabled Start-ups (Day 4)

Graph Theory (Day 5)