Title: Free Resolutions of Monomial Ideals III.
Abstract: We continue the study of resolutions of monomial ideals.
We start with a short proof of the exactness of the Koszul complex. We
then generalize this to free resolutions of any monomial ideal. We'll
conclude with the proof of the Hilbert syzygy theorem and some more
examples of monomial ideals.
Title: Tropical geometry of curves
Abstract: Perhaps surprisingly, the study of degenerate curves plays a
crucial role in our understanding of a general smooth curve. One of the
first successes of this idea was the theory of limit linear series
developed by Griffiths and Harris which they used to prove the
Brill-Noether theorem. The analogous theory for degenerate curves of
non-compact type falls in the realm of tropical geometry where it takes the
shape of metric graphs (or tropical curves) and divisors on them. This
leads to a rich interplay between graph theory and algebraic geometry of
curves. After explaining the central ideas we will discuss some
applications to Brill-Noether theory and curves of large theta
characteristic.
Title: Developments in Fractional Dynamical Systems
Abstract: Fractional calculus (FC) is witnessing rapid development in
recent past. Due to its interdisciplinary nature, and applicability it has
become an active area of research in Science and Engineering. Present talk
deals with our work on fractional order dynamical systems (FODS), in
particular on local stable manifold theorem for FODS. Further we talk on
bifurcation analysis and chaos in the context of FODS. Finally we
conjecture a generalization of Poincare-Bendixon for fractional systems.
5:00pm
Time:
11:30am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Title: Free Resolutions of Monomial Ideals III.
Abstract: We continue the study of resolutions of monomial ideals.
We start with a short proof of the exactness of the Koszul complex. We
then generalize this to free resolutions of any monomial ideal. We'll
conclude with the proof of the Hilbert syzygy theorem and some more
examples of monomial ideals.
Time:
2:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Title: Tropical geometry of curves
Abstract: Perhaps surprisingly, the study of degenerate curves plays a
crucial role in our understanding of a general smooth curve. One of the
first successes of this idea was the theory of limit linear series
developed by Griffiths and Harris which they used to prove the
Brill-Noether theorem. The analogous theory for degenerate curves of
non-compact type falls in the realm of tropical geometry where it takes the
shape of metric graphs (or tropical curves) and divisors on them. This
leads to a rich interplay between graph theory and algebraic geometry of
curves. After explaining the central ideas we will discuss some
applications to Brill-Noether theory and curves of large theta
characteristic.
Time:
4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Title: Developments in Fractional Dynamical Systems
Abstract: Fractional calculus (FC) is witnessing rapid development in
recent past. Due to its interdisciplinary nature, and applicability it has
become an active area of research in Science and Engineering. Present talk
deals with our work on fractional order dynamical systems (FODS), in
particular on local stable manifold theorem for FODS. Further we talk on
bifurcation analysis and chaos in the context of FODS. Finally we
conjecture a generalization of Poincare-Bendixon for fractional systems.