- Time:
- 11:45am - 1:00pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
- Commutative Algebra and Algebraic Geometry seminar.

Speaker: R.V. Gurjar.

Affiliation: IIT Bombay.

Date and Time: Tuesday 04 February, 11:45 am - 01:00 pm.

Venue: Room 113, Department of Mathematics.

Title: P. Griffith's results about abelian covers of regular local rings.

Abstract: We will discuss a structure theorem of a factorial abelian

extension of a regular local ring.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Madhusudan Manjunath.

Affiliation: IIT Bombay.

Date and Time: Tuesday 04 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: A Gentle Introduction to Tropical Algebraic Geometry.

Abstract: We will start with the foundations of tropical algebraic

geometry and then give a glimpse of its applications to algebraic and

arithmetic geometry. The talk will be accessible to PhD students.

- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar.

Speaker: Pranabendu Misra.

Affiliation: Max-Planck Institute for Informatics.

Date and Time: Wednesday 05 February, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Deterministic Representation of Linear Matroids.

Abstract: Matroids are combinatorial objects that generalize the notion of

linear independence. They have several applications in design and analysis

of algorithms. Linear matroids are a subclass of matroids that can be

represented by a matrix. Recently, these matroids have found applications

in Parameterized Complexity, including some breakthrough results. In this

talk, we will discuss the problem of constructing a matrix representation

of linear matroids, especially via deterministic algorithms.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Siva Athreya.

Affiliation: Indian Statistical Institute, Bangalore.

Date and Time: Wednesday 05 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Dense Networks: Sampling and Dynamics.

Abstract: Understanding hidden populations governed by an underlying

network has always been a challenge using standard sampling methods. The

reasons being cost, lack of sampling frame, privacy concerns, and

populations constituting a small proportion. A network is dense if the

number of edges scales quadratically with the number of vertices. In this

talk we shall discuss limitations of a particular sampling procedure

called Respondent Driven Sampling intended to understand hidden

populations and a natural class of dynamics in dense networks arising from

such re-sampling in multi-type population.

- Time:
- 11:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic Geometry seminar.

Speaker: Anand Sawant.

Affiliation: School of Mathematics, TIFR.

Date and Time: Thursday 06 February, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Central extensions of algebraic groups, II.

Abstract: This talk will be a continuation of the Colloquium talk last

week, where we will begin wth the work of Brylinski-Deligne.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Mrinmoy Datta.

Affiliation: Arctic University of Norway, Tromso.

Date and Time: Thursday 06 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Hermitian surfaces over finite fields and a conjecture by Sørensen.

Abstract: Hermitian varieties, first studied by Bose and Chakravati in

1966, are a class of vastly studied objects in the area of finite geometry

and coding theory. During 1991, in his PhD thesis, A. B. Sørensen proposed

a conjecture on the maximum number of rational points on the intersection

of a Hermitian surface and a surface of degree d defined over the same

field. Edoukou's work in 2006 towards proving the conjecture for d=2

marked the first progress towards this conjecture. In 2018, in a joint

work with Peter Beelen, we have shown that the conjecture is true for d=3.

Finally, in a joint work with Peter Beelen and Masaaki Homma, we have

proved the conjecture completely. In this talk, we will give an account of

these developments.

- Time:
- 2:00pm - 3:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Friday 07 February, 02:00 pm - 03:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No 216 Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Marie-Francoise Roy.

Affiliation: University of Rennes.

Date and Time: Monday 10 February, 04:00 pm - 05:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Hilbert 17th problem: classical proof and recent effectivity results.

Abstract: Hilbert 17th problem is asking whether a non negative polynomial

is always a sum of squares. We discuss Artin’s (1927) positive answer to

this problem and explain why this answer did not provide an effective

method for constructing the sum of squares. We describe primitive

recursive effective results obtained by Kreisel and his students in the

fifties. Finally we explain the first elementary recursive degree bound we

obtain, a tower of five exponentials. A precise bound in terms of the

number and degree of the polynomials and their number of variables is

provided. This is a joint work with Henri Lombardi and Daniel Perrucci.

- Time:
- 2:00pm - 3:15pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Tuesday 11 February, 02:00 pm - 03:15 pm.

Venue: Room 114, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE II.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra and Algebraic Geometry seminar.

Speaker: R.V. Gurjar.

Affiliation: IIT Bombay.

Date and Time: Tuesday 11 February, 03:30 pm - 05:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Different differents.

Abstract: We will discuss Noether (also called homological) different,

Dedekind different, and Kahler different and their relationship with each

other.

- Time:
- 11:00am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Combinatorics Seminar.

Speaker: Anuj Vora.

Affiliation: Systems and Control Dept., IIT Bombay.

Date and Time: Wednesday 12 February, 11:00 am - 12:30 pm.

Venue: Room 114, Department of Mathematics.

Title: Zero Error Strategic Communication.

Abstract: We consider a setting between a sender and a receiver, where the

receiver tries to exactly recover a source sequence privately known to the

sender. However, unlike the usual setting of communication, the sender

here aims to maximize its utility and may have an incentive to lie about

its true information. We show that the maximum number of sequences that

can be recovered by the receiver grows exponentially and is given by the

largest independent set of a graph defined on sequences. We then define a

notion of the strategic capacity of a graph and show that it is lower

bounded by the independence number of a suitably defined graph on the

alphabet. Moreover, the Shannon capacity of the graph is an upper bound on

the capacity. This talk will briefly discuss the Shannon's zero-error

capacity problem. We then proceed to derive bounds on the strategic

capacity and give exact values for perfect graphs. If time permits, we

will also discuss the case where the receiver aims for asymptotically

vanishing probability of error.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 105 Department of Mathematics
- Description:
- Probability seminar.

Speaker: Kartick Adhikari.

Affiliation: I.I.T Technion, Israel.

Date and Time: Thursday 13 February, 04:00 pm - 05:00 pm.

Venue: Room 105, Department of Mathematics.

Title: The Spectrum of Dense Random Geometric Graphs.

Abstract: We study the spectrum of Laplacian of a random geometric graph,

in a regime where the graph is dense and highly connected. As opposed to

other random graph models (e.g. the Erdos-Renyi random graph), even when

the graph is dense, not all the eigenvalues are concentrated around 1. In

the case where the vertices are generated uniformly in a unit

d-dimensional box, we show that for every $0\le k \le d$ there are

$\binom{d}{k}$ eigenvalues at $1-2^{-k}$. The rest of the eigenvalues are

indeed close to 1. The spectrum of the graph Laplacian plays a key role in

both theory and applications. Aside from the interesting mathematical

phenomenon we reveal here, the results of this paper can also be used to

analyze the homology of the random Vietoris-Rips complex via spectral

methods.

The talk will be based on a joint work with R. Adler, O. Bobrowski and R.

Rosenthal.

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: Vivek Tewary.

Affiliation: IIT Bombay.

Date and Time: Friday 14 February, 02:30 pm - 03:30 pm.

Venue: Room 114, Department of Mathematics.

Title: Bloch wave approach to almost periodic homogenization.

Abstract: Bloch wave homogenization is a spectral method for obtaining

effective coefficients for periodically heterogeneous media. This method

hinges on the direct integral decomposition of periodic operators, which

is not available in a suitable form for almost periodic operators. In

particular, the notion of Bloch eigenvalues and eigenvectors does not

exist for almost periodic operators. However, we are able to recover the

homogenization result in this case, by employing a sequence of periodic

approximations to almost periodic operators. Another approach, that

employs periodic lifting of quasiperiodic operators is also discussed. We

also establish a rate of convergence for approximations of homogenized

tensors for a class of almost periodic media

- Time:
- 3:30pm - 4:45pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Monday 17 February, 03:30 pm - 04:45 pm.

Venue: Room 215, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE III.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: Tony Joseph Puthenpurakal.

Affiliation: IIT Bombay.

Date and Time: Tuesday 18 February, 03:30 pm - 05:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Localization of complete intersections.

Abstract: We give an elementary proof of the fact that localization of

complete intersection are complete intersections

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Madhusudan Manjunath.

Affiliation: IIT Bombay.

Date and Time: Tuesday 18 February, 04:30 pm - 05:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Introduction to Tropical Algebraic Geometry, Part II: Applications.

Abstract: We will give a glimpse of applications of tropical geometry to

algebraic geometry, particularly the theory of algebraic curves. We will

also mention some potential topics for future work. The talk will not

assume any special background, PhD and MSc students are specially welcome

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar.

Speaker: Murali K. Srinivasan.

Affiliation: IIT Bombay.

Date and Time: Wednesday 19 February, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: A simple recursive algorithm for computing the zonal characters of

the symmetric group (= eigenvalues of the perfect matching association

scheme).

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Wednesday 19 February, 02:30 pm - 03:45 pm.

Venue: Room 215, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE IV.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium I.

Speaker: Mythily Ramaswamy.

Affiliation: Chennai Mathematical Institute.

Date and Time: Wednesday 19 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Time Periodic flows and their stabilization.

Abstract: Fluid flows have been studied for a long time, with a view to

understand better the models like channel flow, blood flow, air flow in

the lungs etc. Here we focus on a time periodic fluid flow model. Local

stabilization here concerns the decay of the perturbation in the flow near

a periodic trajectory. The main motivating example is the incompressible

Navier-Stokes system. I will discuss the general framework to study

periodic solutions and then indicate some results in this direction.

- Time:
- 2:00pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar.

Speaker: Nishad Kothari.

Affiliation: Institute of Computing, Campinas, Brazil.

Date and Time: Thursday 20 February, 02:00 pm - 3:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Generation Theorems for Bricks and Braces.

Abstract:

A connected graph G, on two or more vertices, is matching covered if each edge belongs to

some perfect matching. For problems pertaining to perfect matchings of a graph — such as

counting the number of perfect matchings — one may restrict attention to matching covered

graphs.

Every matching covered graph may be decomposed into a list of special matching covered

graphs called bricks (nonbipartite) and braces (bipartite); Lov´asz (1987) proved that this

decomposition is unique. The significance of this decomposition arises from the fact that

several important open problems in Matching Theory may be reduced to bricks and braces.

(For instance, a matching covered graph G is Pfaffian if and only if each of its bricks and

braces is Pfaffian.) However, in order to solve these problems for bricks and braces, one needs

induction tools; these may also be viewed as generation theorems for bricks and braces.

Norine and Thomas (2007) proved a generation theorem for simple bricks. In a joint work

with Murty (2016), we used their result to characterize K4-free planar bricks. However, it

seems very difficult to characterize K4-free nonplanar bricks. For this reason, I decided to

develop induction tools for a special class of bricks called ‘near-bipartite bricks’.

A brick G is near-bipartite if it has a pair of edges {α, β} such that G−α−β is matching

covered and bipartite. During my PhD, I (https://onlinelibrary.wiley.com/doi/10.

1002/jgt.22414) proved a generation theorem for near-bipartite bricks. In a joint work with

Carvalho (https://arxiv.org/abs/1704.08796), we used this result to prove a generation

theorem for simple near-bipartite bricks. Our theorem states that all near-bipartite bricks

may be built from 8 infinite families by means of (a finite sequence of) three operations.

McCuaig (2001) proved a generation theorem for simple braces, and used it to obtain

a structural characterization of Pfaffian braces — thus solving the Pfaffian Recognition

Problem for all bipartite graphs. A brace is minimal if removing any edge results in a graph

that is not a brace. In a recent work with Fabres and Carvalho (https://arxiv.org/abs/

1903.11170), we used McCuaig’s brace generation theorem to deduce an induction tool for

minimal braces. As an application, we proved that a minimal brace with 2n vertices has at

most 5n − 10 edges, when n ≥ 6, and we obtained a complete description of minimal braces

that meet this upper bound.

I will present the necessary background, and describe our aforementioned results. The

talk will be self-contained. I shall assume only basic knowledge of graph theory, and will not

present any lengthy proofs.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium II.

Speaker: Stefan Schwede.

Affiliation: University of Bonn.

Date and Time: Thursday 20 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Equivariant properties of symmetric products.

Abstract: The ultimate aim of this talk is to explain a calculation of

equivariant homotopy groups of symmetric products of spheres. To lead up

to this, I will review the notion of degree of a map between spheres, and

of its equivariant refinement, for a finite group G of equivariance. The

answer is best organized as an isomorphism, due to Graeme Segal, to the

Burnside ring of the finite group G.

The filtration of the infinite symmetric product of spheres by number of

factors has received a lot of attention in algebraic topology. We

investigate this filtration for spheres of linear representations of the

finite group G; by Segal's theorem, the resulting sequence of 0th

equivariant homotopy groups starts with the Burnside ring, and it ends in

a single copy of the integers (independent of the group of equivariance).

We describe this sequence in a uniform and purely algebraic manner,

including the effect of restrictions and transfers maps that connect the

values for varying groups G.

An effort will be made to make a good portion of the talk accessible to

graduate students.

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Nitin Nitsure.

Date and Time: Monday 24 February, 03:30 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Cotangent complex and applications (A short series of lectures).

Abstract: Differential 1-forms are very useful in the study of

multivariate calculus or smooth manifolds. Algebraically, the module of

Kahler differentials is very useful in commutative algebra. When the

spaces (or varieties) are not smooth but have singularities, differential

1-forms are not enough. Instead there is available a more general gadget

called the cotangent complex in commutative algebra as well as in

algebraic geometry. This series of talks will begin by recalling usual

differential forms and Kahler differentials in familiar setting, and then

introduce the cotangent complex. Applications to smoothness, local

complete intersections and deformation theory will be shown. Some

familiarity with the language of commutative algebra will be assumed.

The first talk will be accessible to advanced undergraduate students.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. G01, Computer Center (CC) Conference Room
- Description:
- Partial Differential Equations seminar (via videoconference).

Speaker: Martina Hofmanova.

Affiliation: Bielefeld University.

Date and Time: Tuesday 25 February, 04:00 pm - 05:00 pm.

Venue: Room No. G01, Computer Center (CC) Conference Room.

Title: Non-uniqueness in law of stochastic 3D Navier-Stokes equations

Abstract: I will present a recent result obtained together with R. Zhu and

X. Zhu. We consider the stochastic Navier-Stokes equations in three

dimensions and prove that the law of analytically weak solutions is not

unique. In particular, we focus on two iconic examples of a stochastic

perturbation: either an additive or a linear multiplicative noise driven

by a Wiener process. In both cases, we develop a stochastic counterpart of

the convex integration method introduced recently by Buckmaster and Vicol.

This permits to construct probabilistically strong and analytically weak

solutions defined up to a suitable stopping time. In addition, these

solutions fail the corresponding energy inequality at a prescribed time

with a prescribed probability. Then we introduce a general probabilistic

construction used to extend the convex integration solutions beyond the

stopping time and in particular to the whole time interval [0,∞].

Finally, we show that their law is distinct from the law of solutions

obtained by Galerkin approximation. In particular, non-uniqueness in law

holds on an arbitrary time interval [0,T], T>0.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Statistics and Probability seminar.

Speaker: Nilanjan Chatterjee.

Affiliation: Johns Hopkins University.

Date and Time: Wednesday 26 February, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Statistical model building using data fusion.

Abstract: Many applications require development of complex statistical

models involving many variables. It may not, however, be possible to train

such model in a single dataset of adequately large sample size that has

measured all the variables. Instead, data may be available across multiple

studies, where any individual study may not measure all the variables, but

the different studies altogether cover all the variables. In this talk, I

will describe how to fit popular non-linear models, such as logistic

regression models, by combining information from such multiple disparate

data sources. In fact we will show it is possible to fit such models only

using "summary-level" information, i.e. estimates of parameters from

fitted simpler models, from individual studies and thus overcoming some

of the logistical and ethical issues related to sharing of individual

level data across studies. Methods will be illustrated through extensive

simulation studies and real data examples

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Arjun Paul.

Affiliation: IIT Bombay.

Date and Time: Wednesday 26 February, 02:30 pm - 03:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Fundamental group schemes of Hilbert scheme of n points on

irreducible smooth projective varieties of dimension 1 and 2.

Abstract: : Let k be an algebraically closed field of characteristic p > 3. Let X be an irreducible

smooth projective k-variety of dimension d ∈ {1, 2} over k. Fix an integer n ≥ 2, and let

Hilbn

X be the Hilbert scheme parametrizing effective 0-cycles of length n on X. In this talk

we discuss on the S-fundamental group scheme and Nori’s fundamental group scheme of

Hilbn

X. This is a joint work with Ronnie Sebastian.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Nilanjan Chatterjee.

Affiliation: Johns Hopkins University.

Date and Time: Wednesday 26 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Disease risk prediction and causal inference using genome-wide

genetic data.

Abstract: Recent genome-wide association studies have led to

identification of thousands of genetic variants associated with complex

traits and diseases like adult height, body mass index, heart disease,

type-2 diabetes and cancer. The large scale genetic data, some of which

are publicly available, provide statisticians, mathematicians, computer

scientists and other quantitative researchers an incredible opportunity

for the development and applications of novel methods and algorithms. In

this talk, I will describe the work from our laboratory to harness the

power of these big datasets to address two most pressing problems in

public health research. In particular, I will describe simple and more

advanced machine learning methods for building genetic risk-scores from

these datasets that can be used to predict prospectively individuals' risk

of diseases. Further, I will describe how genetic data can be used to

conduct, "instrumental" variable analysis, an approach popular in

Economics, to understand causal relationship among risk-factors and health

outcomes.

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Madhusudan Manjunath.

Affiliation: IIT Bombay.

Date and Time: Thursday 27 February, 04:30 pm - 05:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Introduction to Tropical Algebraic Geometry, Part II: Applications.

Abstract: We will give a glimpse of applications of tropical geometry to

algebraic geometry, particularly the theory of algebraic curves. We will

also mention some potential topics for future work. The talk will not

assume any special background, PhD and MSc students are specially welcome.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic Geometry seminar.

Speaker: Amit Tripathi.

Affiliation: IIT Hyderabad.

Date and Time: Friday 28 February, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Vector bundles over complex projective hypersurfaces.

Abstract: In the first half of this talk I will discuss some results

related to existence (or rather non existence) of indecomposable low rank

vector bundles over complex projective space followed by similar questions

for hypersurfaces. The second half will be devoted to a generic version of

the BGS conjecture for ACM bundles on hypersurfaces and a recent joint

work with Girivaru Ravindra.