Siddhartha Gadgil

Department of Mathematics
Indian Institute of Science
Bangalore 560012, India

e-mail: gadgil@math.iisc.ernet.in

• MA 220: Mathematical Logic and Computability

Research

My research is primarily in Low-dimensional Topology and related areas such as Geometric Group theory, Symplectic Topology, Metric and Riemannian Geometry. I have also applied topology to Molecular Biology.

• My  CV.

Papers - Accepted and Appeared

• Open manifolds, Ozsvath-Szabo invariants and Exotic $\R^4$'s, Expo. Math. 28 (2010), no. 3, 254-261.
• Surfaces of bounded mean curvature in Riemannian manifolds , Trans. Amer. Math. Soc. 363 (2011), 3977-4005.
• Algebraic and Geometric Intersection numbers for free groups (joint with Suhas Pandit), to appear in Topology and its Applications. 
• Real theta characteristics and automorphisms of a real curve (joint with Indranil Biswas), J. Aust. Math. Soc. 88 (2010), 29-42.
• Watson-Crick pairing, the Heisenberg group and Milnor invariants, Journal of Mathematical Biology 59 (2009), 123-142.
• On the topology of manifolds with positive isotropic curvature, Proc. Amer. Math. Soc. 137 (2009),  1807-1811.
• Least-area surfaces and Incompressibility, Expos. Math. 26 (2008), no. 1, 93-98.
• Non-orientable Thom-Pontrjagin constructions and Seifert surfaces (joint with Dishant Pancholi), J. Ramanujan Math. Soc. 23 (2008), no. 2, 143-149.
• On theta characteristics of a compact Riemann surface (joint with I. Biswas and P. Sankaran), Bull. Sci. Math. 131 (2007), no. 5, 493--499.
• Degree-one maps, Surgery and four-manifolds, Bull. Lond. Math. Soc. 39 (2007), no. 3, 419-424.
• Embedded spheres in S^2\times S^1#...#S^2\times S^1, Topology Appl. 153 (2006), no. 7, 1141--1151.
• The Chord algebra and fundamental groups (joint with Lenny Ng), appendix to Knot and braid invariants from contact homology II by Lenny Ng, Geom. Topol. 4 (2005), 1603-1637.
• On the geometric simple connectivity of open manifolds. (joint with Louis Funar) Int. Math. Res. Not. (2004), no. 24, 1193--1248.
• Contact structures on elliptic 3-manifolds. Proc. Amer. Math. Soc. 132 (2004), no. 12, 3705--3714
• Limits of functions and elliptic operators, Proc. Indian Acad. Sci. Math. Sci. 114 (2004), no. 2, 153--158.
• Homology and homeomorphisms of non-orientable surfaces (joint with Dishant Pancholi), Proc. Indian Acad. Sci. Math. Sci. 115 (2005), no. 3, 251--257.
• Extremes of the Indian summer monsoon , (joint with Sulochana Gadgil, P.N. Vinaychandran and P.A. Francis) Geophysical Research letters 2004.
• Equivariant framings, lens spaces and contact structures. Pacific J. Math. 208 (2003), no. 1, 73--84.
• Cobordisms and Reidemeister torsions of homotopy lens spaces, Geom. Topol. 5 (2001), 109-125.
• The $pq$-condition for $3$-manifold groups , Proc. Amer. Math. Soc. 129 (2001), no. 6, 1873-1875.
• Topological geodesics and virtual rigidity (joint with Louis Funar), Algebr. Geom. Topol. 1 (2001), 369-380.

Preprints

• A triangulation of a homotopy Deligne-Mumford compactification of Moduli space,  submitted for publication.
• A chain complex and quadrilaterals for normal surfaces (joint with Tejas Kalelkar), submitted for publication.
  
• One-handles and Concordance kernels of smooth 4-manifolds, submitted for publication..
• Degree-one maps and Akbulut corks, preprint.
• On the Andrews-Curtis conjecture and algorithms from topology, preprint
• The derived series and virtual Betti numbers., preprint
• Conformal structures and harmonic functions (joint with Harish Seshadri), preprint

Expository articles

For a general scientific audience.

• Ricci flow and the Poincare conjecture : joint with Harish Seshadri.
• Dynamics on the circle : article in Resonance.
• Symmetries of spheres : PDF slides for a lecture to the Indian Academy of Sciences (not designed to be self-contained).
• Chern and total curvature , article in Resonance.

More technical

• A topological characterisation of hyperbolic spaces (following Bowditch).
• Knotted Tori.
• Lectures notes on 3-manifold topology: Connected sums and prime decompositions, Heegaard splittings and Dehn surgery .
• Lecture notes on delta-hyperbolic spaces