Contact informationMailing Address: Amitabh Basu Department of Applied Mathematics and Statistics Johns Hopkins University Wyman Park Building, Room S438 3400 North Charles Street Baltimore, MD 21218 Department office: Wyman S438 Phone: 410-516-7582 Email: basu.amitabh[AT]jhu[DOT]edu |

I'm a Professor in the Applied Mathematics and Statistics department, with a secondary appointment in the Computer Science department, at Johns Hopkins University. I obtained my PhD in the ACO program at Carnegie Mellon University, advised by Gerard Cornuejols. My research interests lie in Optimization (with current emphasis on Integer Programming), Discrete and combinatorial geometry, and Convex analysis, and the applications of these tools in Operations Research, Astronomy and Data Science.

Heard while eavesdropping on a mathematician: "These schemes are pointless"

Area Editor,

Associate Editor,

Organizing committee member,

Associate Editor,

Editorial board member,

Associate Editor,

Associate Editor,

Program Committee,

Program Committee,

Vice Chair (Integer and Discrete Optimization),

Chair, Program Committee,

Program Committee,

Program Committee,

Chair, Local organization committee,

AMS 553.465/665: Introduction to Convexity (Fall 2016, 2017, 2018, 2022, 2023, Spring 2024)

AMS 553.766: Combinatorial Optimization (Fall 2013, 2014, 2015, Spring 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024)

AMS 553.761: Nonlinear Optimization I (Fall 2018, 2019, 2020, 2022)

AMS 553.472/672: Graph Theory (Spring 2014, 2015, 2016)

MAT 25 (Spring 2013)

MAT 17B (Fall 2011, Spring 2012, Fall 2012)

MAT 165 (Fall 2012)

MAT 16A (Spring 2012)

MAT 16B (Spring 2011)

MAT 16C (Spring 2011)

In the 2010-2011 session, I led an RFG on Applications of Convex Geometry, as part of the NSF funded VIGRE program of the Department of Mathematics. Some lecture notes from the Fall session. The Winter quarter activities are recorded here. The Spring activities will be updated on this page.

Advanced Integer Programming (Spring 2010)

Learning cut generating functions for integer programming,

Sample complexity of algorithm selection using neural networks and its applications to branch-and-cut,

On the power of graph neural networks and the role of the activation function,

A universal transfer theorem for convex optimization algorithms using inexact first-order oracles, (with P. Kerger, M. Molinaro, H. Jiang),

Information complexity of mixed-integer convex optimization, (with H. Jiang, P. Kerger, M. Molinaro),

Neural networks with linear threshold activations: structure and algorithms, (with S. Khalife and H. Cheng),

Complexity of optimizing over the integers,

Complexity of branch-and-bound and cutting planes in mixed-integer optimization, (with M. Conforti, M. Di Summa and H. Jiang),

Complexity of branch-and-bound and cutting planes in mixed-integer optimization -- II, (with M. Conforti, M. Di Summa and H. Jiang),

Two-halfspace closure, (with H. Jiang),

Distance-based Positive and Unlabeled Learning for Ranking, (with H. S. Helm, A. Athreya, Y. Park, J. T. Vogelstein, M. Winding, M. Zlatic, A. Cardona, P. Bourke, J. Larson, C. White, C. E. Priebe),

Neural networks with linear threshold activations: structure and algorithms, (with S. Khalife),

Globally optimal and scalable N-way matching of astronomy catalogs, (with T. Nguyen, T. Budavari),

Enumerating integer points in polytopes with bounded subdeterminants, (with H. Jiang),

Towards Lower Bounds on the Depth of ReLU Neural Networks, (with C. Hertrich, M. Di Summa, M. Skutella),

Split cuts in the plane, (with M. Conforti, M. Di Summa and H. Jiang),

Admissibility of solution estimators for stochastic optimization, (with T. Nguyen and A. Sun),

Mixed-integer bilevel representability, (with C. Ryan and S. Sriram),

Optimal Probabilistic Catalogue Matching for Radio Sources, (with D. Fan, T. Budavari, R. Norris),

An extreme function which is nonnegative and discontinuous everywhere, (with M. Conforti and M. Di Summa),

The structure of the infinite models in integer programming, (with M. Conforti, M. Di Summa, and J. Paat),

Mixed-integer linear representability, disjunctions, and variable elimination -- modeling implications, (with K. Martin, C. Ryan, and G. Wang),

Optimal cutting planes from the group relaxations, (with M. Conforti, M. Di Summa and G. Zambelli),

Robust registration of astronomy catalogs with applications to the Hubble Space Telescope, (with F. Tian, T. Budavari, S. Lubow, and R. White),

Non-unique lifting of integer variables in minimal inequalities, (with S. Dey and J. Paat),

Can cut generating functions be good and efficient?, (with S. Sriram),

Probabilistic cross-identification of multiple catalogs in crowded fields, (with X. Shi and T. Budavari),

Approximation of minimal functions by extreme functions, (with T. Lebair),

Sparse coding and autoencoders, (with A. Rangamani, A. Mukherjee, T. Ganapathy, A. Arora, S. Chin, and T. D. Tran),

Understanding Deep Neural Networks with ReLUs, (with R. Arora, P. Mianjy, and A. Mukherjee),

Extreme Functions with an Arbitrary Number of Slopes, (with M. Conforti, M. Di Summa and J. Paat),

Minimal cut-generating functions are nearly extreme, (with M. Molinaro and R. Hildebrand),

Approximation of corner polyhedra with families of intersection cuts, (with G. Averkov, J. Paat),

Optimality certificates for convex minimization and Helly numbers, (with M. Conforti, G. Cornuejols, R. Weismantel, S. Weltge),

Centerpoints: A link between optimization and convex geometry, (with T. Oertel),

Strong duality and sensitivity analysis in semi-infinite linear programming, (with K. Martin and C. Ryan),

Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2, (with R. Hildebrand, M. Koeppe),

Galaxy Redshifts from Discrete Optimization of Correlation Functions, (with B. Lee, T. Budavari and M. Rahman),

Probabilistic Cross-Identification in Crowded Fields as an Assignment Problem, (with T. Budavari),

Computing approximate PSD factorizations, (with M.Dinitz and X. Li),

Light on the infinite group relaxation, (with R. Hildebrand, M. Koeppe),

Operations that preserve the covering property of the lifting region, (with J. Paat),

Lifting Properties of Maximal Lattice-free Polyhedra, (with G. Averkov),

A geometric approach to cut-generating functions, (with M. Conforti, M. Di Summa),

Characterization of the Split Closure via Geometric Lifting, (with M. Molinaro),

Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming, (with K. Martin, C. Ryan),

Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem I. The One-Dimensional Case, (with R. Hildebrand, M. Koeppe),

On the Unique-lifting Property, (with G. Averkov),

The Triangle Closure is a Polyhedron, (with R. Hildebrand, M. Koeppe),

On Chubanov's method for Linear Programming, (with J. De Loera, M. Junod),

On the sufficiency of finite support duals in semi-infinite linear programming, (with K. Martin, C. Ryan),

Equivariant Perturbations for Gomory and Johnson's Infinite Group Problem. II. The Unimodular Two Dimensional Case, (with R. Hildebrand, M. Koeppe),

A (k+1)-Slope Theorem for the k-Dimensional Infinite Group Relaxation, (with R. Hildebrand, M. Koeppe, M. Molinaro),

Unique lifting of integer variables in minimal inequalities, (with M. Campelo, M. Conforti, G. Cornuejols, G. Zambelli),

A Counterexample to a Conjecture by Gomory and Johnson, (with M. Conforti, G. Cornuejols and G. Zambelli)

Unique Minimal Liftings for Simplicial Polytopes, (with G. Cornuejols and M. Koeppe),

Intersection cuts with Infinite Split Rank, (with G. Cornuejols and F. Margot)

A Probabilistic Analysis of the Strength of Split and Triangle Closures, (with G. Cornuejols and M. Molinaro) IPCO 2011 version,

Experiments with two row cuts from degenerate tableaux, (with P. Bonami, G. Cornuejols and F. Margot)

Convex Sets and Minimal Sublinear Functions, (with G. Cornuejols and G. Zambelli)

Maximal Lattice-free Convex Sets in Linear Subspaces, (with M. Conforti, G. Cornuejols and G. Zambelli)

Minimal Inequalities for an Infinite Relaxation of Integer Programs, (with M. Conforti, G. Cornuejols and G. Zambelli)

On the Relative Strength of Split, Triangle and Quadrilateral Cuts, (with P. Bonami, G. Cornuejols and F. Margot)

Geometric Algorithms for Optimal Airspace Design and Air Traffic Controller Workload Balancing, (with J.S.B. Mitchell and G. Sabhnani)

Distributed Localization using Noisy Distance and Angle Information, (with J. Gao, J.S.B. Mitchell and G. Sabhnani)

Security types preserving compilation, (with G. Barthe and T. Rezk)

Helly systems and certificates in optimization, (with T. Chen, M. Conforti and H. Jiang)

A perspective on human and artificial intelligence

Notes on Lasserre hierarchies, SOS relaxations and pseudo-expectations

An exposition of special relativity without appeal to "constancy of speed of light" hypotheses

Introduction to Convexity

Lower bounds over Boolean inputs for deep neural networks with ReLU gates, (with A. Mukherjee)

Lectures on Modern Approaches to Cutting Planes

Maximal Lattice-free Convex Sets in 3 Dimensions (with Gerard Cornuejols and Francois Margot)

Steiner Point Removal in Graph Metrics (with Anupam Gupta)