Topic Name
Talk Title Talk Abstract Date, Time, Venue

Session IB (Applied Math)

Angelyn Lao The Mathematics of Reaction Network and Its Applications to Systems Biology The Mathematics of Reaction Network (MoRN) relates the topological features of a network to the qualitative properties of the corresponding system of ordinary differential equations (ODE). In systems biology, most of the models that are established to reflect the effects of variations in biological processes are ODE-based where parameter uncertainty is predominant. A quantitative tool like MoRN shows potential benefits in studying biological systems without relying on parameter values. In this talk, I will give a brief introduction to MoRN and exhibit how it is applied in Systems Biology.

Tuesday, 25 April
Ramanujan Lecture Hall

Jyoti U. Devkota Statistical Analysis of Gender Gap in Education and Employment - with examples from Nepal Women are 50% of the population. If this section lags behind in education and opportunity, then half of the world is deprived of opportunities.
This lag also affects science and technology, which has adverse impact on society at every level. Efforts should be made to reduce this gap.
“Achieve gender equality and empower all women and girls” is also one of the seventeen United Nations Sustainable Development Goals. So data
based studies related to the gender gap in science and technology need to be conducted, as what get’s measured also should get done. With 66%
of people being employed in agriculture sector, the economy of Nepal is agricultural based. This workforce is mainly dominated by women. As
men are migrating abroad for lucrative and well paid jobs, the contribution of women in the workforce has increased from 36% in 1981 to 45%
1991. This number has further soared to 50% in 2017. But the percentage of women with ownership of land is only 20%. In this paper, gender gap
in education and employment sector in Nepal is analyzed. Government schools and Universities of Nepal are considered here for education sector.
The dynamics of change in gender gap with respect to subject of education and sector of employment is modelled with respect to Multinomial
Logistic Regression and Odds Ratio. The results are based on secondary data collected by the government [1] and primary data collected for this
Keywords: Statistical Analysis, Logistic Regression, Odds Ratio, Gender Gap.
1. MOE, (2017): Education in Figures 2017. Kathmandu: Ministry of Education, Government of Nepal, Singh Durbar, Kathmandu, Nepal.
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Ikha Magdalena Partial Differential Equations for Investigating Mangroves Forest to Combat Climate Change Climate change can lead to increase storm surges and sea-level rise that can cause erosion along coastlines. Erosion can have serious consequences, such as loss of land, damage to infrastructure, and harm to ecosystems. Mangroves, on the other hand, are known to be highly effective at mitigating erosion along coastline. In this research, we investigate the effectiveness of Mangrove Forest to protect the shoreline from erosion through a mathematical model. The mathematical model we construct is a hyperbolic partial differential equation. We solve the model analytically to obtain the wave transmission coefficient. This coefficient gives us information about how much damping caused by the mangroves. To simulate over a complex topography, we also solve the model numerically using a staggered finite volume method. This method is free from damping error that is important in this study to calculate the wave attenuation by the mangroves. For validation, we will compare the numerical results with the analytical solution and experimental data.
Sohyun Jeon* Practical Randomized Lattice Gadget Decomposition With Application to FHE Gadget decomposition is widely used in lattice based cryptography, especially homomorphic encryption (HE) to keep the noise growth slow. If it is randomized following a subgaussian distribution, it is called subgaussian (gadget) decomposition which guarantees that we can bound the noise contained in ciphertexts by its variance. This gives tighter and cleaner noise bound in average case, instead of the use of its norm. Even though there are few attempts to build efficient such algorithms, most of them are still not practical enough to be applied to homomorphic encryption schemes due to somewhat high overhead compared to the deterministic decomposition. Furthermore, there has been no detailed analysis of existing works. Therefore, HE schemes use the deterministic decomposition algorithm and rely on a Heuristic assumption that every output element follows a subgaussian distribution independently.
In this work, we introduce a new practical subgaussian gadget decomposition algorithm which has the least overhead (less than 14\%) among existing works for certain parameter sets. When the modulus is large (over 100-bit), our algorithm is not always faster than the other similar work. Therefore, we give a detailed comparison, even for large modulus, with all the competitive algorithms for applications to choose the best algorithm for their choice of parameters.
Jaeseon Kim* CPA-to-CCA Transformation for Lattice based KEM without random oracle In the random oracle model, cryptosystems can easily be designed and proved their security. Random oracle is actually implemented using a secure hash function because it is hard to build that. But it is mistrust because secure hash function does not imply random oracle. Therefore, achieving IND-CCA secure KEM in the standard model is an active research topic even though they are less efficient so various research on this topic is being studied at the same time. We optimized one of them to be applied to lattice-based cryptosystems, and as a result, we propose the first generic transformation to convert a lattice-based IND-CPA secure KEM to IND-CCA. Our generic transformation reduced the complexity of encapsulation, the most expensive part of the previous paper down to constant from poly(n), where n is the security parameter via using uniform hash functions. Furthermore, we provide an instantiation based on the lattice problem.

Session IA (Misc)

Carlene P.C. Pilar-Arceo Applying a River Water Quality Model to the Philippines’ Pasig River This talk presents a reaction-based numerical model simulating sediment and reactive chemical transport in rivers involving both kinetic and equilibrium reactions. and its possible application to a Philippine river system, the Pasig River. A reactive transport equation is developed and solved using the fully implicit finite element method. The applicability to Pasig River data is explored as a potential gateway to applying the model and methods to different river systems in the country and, hopefully, recommending interventions beneficial to river water quality.

Tuesday, 25 April
Madhava Lecture Hall


Mousumi Mandal* Study of symbolic powers of edge ideals of weighted oriented graphs. In this talk we discuss the symbolic powers of weighted oriented graphs.
We give necessary and sufficient conditions for the equality of symbolic power and
ordinary power for the edge ideals of certain classes of weighted oriented graphs.
We characterize the weighted naturally oriented unicyclic graphs with unique odd
cycles and weighted naturally oriented even cycles for the equality of ordinary and
symbolic powers of their edge ideals.
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Rashi Lunia On Euler-Kronecker Constants The Dedekind zeta function $\zeta_\K(s)$ of a number field $\K$ has a simple pole at $s=1$ with residue $\rho_\K$. Its Laurent
series expansion around $s=1$ is given by
Ihara defined the Euler-Kronecker constant of a number field $\K$ as $\gamma_\K=\frac{c_\K}{\rho_\K}$.
He conjectured that there exists positive constants $a_0, a_1 \leq 2$ such that for $m$ sufficiently large and any $\epsilon>0$, we have
$$(a_0-\epsilon)\log{m}<\gamma_{\Q(\zeta_m)}< (a_1+\epsilon)\log{m}.$$
This bound was shown to hold on average by Fouvry as we vary over a family of cyclotomic fields. In this talk, we elaborate on an
ongoing work where we study the Euler-Kronecker constant of a more general family of number fields and compare our results with
existing bounds.
Jyothsnaa Sivaraman Products of primes in ray classes In 1944, Linnik showed that the least prime in an arithmetic progression
given by $a \bmod q$ for $(a,q)=1$ is at most $cq^L$ for
some absolutely computable constants $c$ and $L$.
A lot of work has gone in computing explicit bounds for
$c$ and $L$. The best known bound is due to Xylouris (2011)
who showed that $c$ can be taken to be $1$ and $L$
to be $5$ for $q$ sufficiently large. In 2018, Ramare and
Walker gave a completely explicit result if one prime
is replaced by a product of primes. They showed that each co-prime class
modulo $q$ contains a product of three primes each less than $q^{16/3}$.
This was improved by Ramar{\'e}, Srivastava and Serra to $650 q^3$ in 2020.
In this talk we will introduce analogous results in the set up of narrow ray class
fields of number fields. This is joint work with Deshouillers, Gun and Ramar{\'e}.
Suhita Hazra ON TWO VARIABLE ARTIN’S CONJECTURE ABSTRACT. In 1927, Artin conjectured that any integer a which is not ́1 or a perfect square
is a primitive root for a positive density of primes p. Though many significant partial results
have been established, we do not have a single integer a which is a primitive root for infinitely
many primes. A variant of Artin’s conjecture, known as the two variable Artin’s conjecture was
introduced by Moree and Stevenhagen in 2000 and they showed that for any two multiplicatively
independent a and b in Q
, the set
tp : p prime, a mod p P xb mod pyu

has positive density under GRH. Unconditional lower bound of the above set was obtained by

Ram Murty, Seguin and Stewart in 2019. In this talk, we will report an ongoing work with Jyoth-
snaa Sivaraman where we improve the lower bounds of Murty-Seguin-Stewart.

Session II A (Misc)

Pallabi Manna* On finite groups whose power graph is self-complementary. In general, a graph is called self-complementary if there exist an isomorphism between the graph and its complement.
Analogously, a graph $\Gamma$ is called self-complementary in the sense of some graph property $P$ if both $\Gamma$ and $\overline{\Gamma}$(complement of $\Gamma$) has the property $P$. We observe that there is no finite group $G$, except possibly $G\ncong C_{n}\rtimes C_{p_{k}^{\alpha_{k}}}$ with $p_{k} \nmid n$ and $C_{n}\rtimes Q_{2^r}$ with $2\nmid n$, whose power graph is self-complementary. Next we discuss about the self-complementary index of power graphs. Moreover, we provide suitable sharp lower and upper bounds for the self-complementary index of such graphs. In addition, we characterize finite groups whose power graphs are self- complementary in the sense of unicyclicity, $2$-connectedness and various forbidden subgraphs.

Thursday, 27 April
Ramanujan Lecture Hall


Rinovin Simayountak* How to uniquely identify a vertex in a graph: a (multiset) metric dimension problem The metric dimension problem was first introduced in 1975 by Slater and independently by Harary and Melter [14] in 1976; however, the problem for hypercube was studied (and solved asymptotically) much earlier in 1963 by Erdos and Renyi. An ordered set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. It has been showed that determining the metric dimension of an arbitrary graph is an NP-complete problem. The problem is still NP-complete even if we consider some specificc families of graphs, such as bipartite graphs or planar graphs. A variation of the metric dimension concept is when every vertex in G is uniquely determined by its multiset of distances to the vertices in S. In this case, S is unordered, and it is called an m-resolving set for G.

In this talk, I will present a short historical account, known techniques, recent results, and open problems in the area of (multiset) metric dimension.

Kriti Goel* Local cohomology of invariant rings Consider a finite group $G$ acting on a polynomial ring $R$ over a field. One of the fundamental problems of invariant theory is to establish a connection between the properties of the invariant ring $R^G$ and the properties of the group action. However, the situation is generally better understood in the situation where the order $|G|$ of the group is invertible. In this talk, we will explore some questions on the local cohomology modules of the ring of invariants in the tricky situation where $|G|$ is not a unit. This is a joint work in progress with Anurag Singh (University of Utah, USA) and Jack Jeffries (University of Nebraska-Lincoln, USA).
Susmita Seal* Small diameter properties in Banach spaces In 1967 Rieffel, Maynard, Huff, Davis and Phelps identified the fundamental relationship between Radon Nikodym Property (RNP) and the geometry of a Banach space. They showed that a Banach space X has RNP if and only if every nonempty closed, bounded, convex subset of X is dentable. Then around 1987 Ghoussoub, Godefroy, Maurey and Schachermayer studied two different geometric properties, weaker than RNP, namely, Point of Continuity Property (PCP) and Strongly Regular (SR). In our work we study the localization of the above mentioned properties RNP, PCP and SR to the closed unit ball of a Banach space and we call these localization small diameter properties of Banach spaces. In this connection we first study the stability of these properties under $l_p$ sum , $c_0$ sum and Lebesgue Bochner spaces. We also show that these are three space properties under certain conditions on the quotient space. It is true that none of these properties are hereditary or lifting. we prove that if $X$ has small diameter property, then each of its $M$-ideal subspace inherits the same and we also showed if $X$ has an almost isometric ideal subspace with small diameter property, then the same property lifts to the whole space $X$. Since the small diameter properties are not hereditary, then the next best thing we can expect is that the spaces with small diameter properties to satisfy is the separably determined property and we prove this in affirmative. This is a joint work with my thesis supervisor Prof. Sudeshna Basu.
Geetika Verma* Frames and Fractals Weaving frames have been introduced to deal with some problems in signal processing and wireless sensor networks. More recently, the notion of fractal operator and fractal convolutions have been linked with perturbation theory of Schauder bases and frames. However, the existing literature has established limited connections between the theory of fractals and frame expansions. In this paper we define Weaving frames generated via fractal operators combined with fractal convolutions. The aim is to demonstrate how partial fractal convolutions are associated to Riesz bases, frames and the concept of Weaving frames. This current view point deals with ones sided convolutions i.e both left and right partial fractal convolution operators on Lebesgue space $L^p$ $(1 \leq p < \infty)$. Some applications via partial fractal convolutions with null function have been obtained for the perturbation theory of bases and weaving frames.
Bhavna Transverse spectral Instabilities in rotation-modified Kadomtsev-Petviashvili equation and related models The rotation-modified Kadomtsev-Petviashvili equation which is also known as the Kadomtsev–Petviashvili–Ostrovsky equation, describes the gradual wave field diffusion in the transverse direction to the direction of the propagation of the wave in a rotating frame of reference. This equation is generalization of the Ostrovsky equation additionally having weak transverse effects. We investigate transverse instability and stability of small periodic traveling waves of the Ostrovsky equation with respect to either periodic or square-integrable perturbations in the direction of wave propagation and periodic perturbations in the transverse direction of motion in the rotation-modified Kadomtsev-Petviashvili equation. We also study transverse stability or instability in generalized rotation-modified KP equation by taking dispersion term as general and quadratic and cubic nonlinearity. As a consequence, we obtain transverse stability or instability in two dimensional generalization of RMBO eqution, Ostrovsky-Gardner equation, Ostrovsky-fKdV equation, Ostrovsky-mKdV equation, Ostrovsky-ILW equation, Ostrovsky-Whitham etc.

Session IIB (PDEs)

Pratibha Shakya Finite Element Methods for Elliptic Optimal Control Problems with Measure Data We analyze both a priori and a posteriori error analysis of finite element method for elliptic optimal control problems with measure data in a bounded convex domain in $\mathbb{R}^d$ $(d=2\;\text{or} \;3)$.
The solution of the state equation of such type of problems exhibits low regularity due to the presence of measure data which introduces some difficulties for both theory and numerics of the finite element method. We first prove the existence, uniqueness, and regularity of the solution to the optimal control problem. To discretize the control problem we use piecewise linear and continuous finite elements for the approximations of the state and co-state variables whereas piecewise constant functions are used for the control variable. We derive a priori error estimates of order $\mathcal{O}(h^{2-\frac{d}{2}})$ for the state, co-state, and control variables in the $L^2$-norm. Further, global a posteriori upper bounds for the state, co-state, and control variables in the $L^2$-norm are established. Moreover, local lower bounds for the errors in the state and co-state variables, and global lower bound for the error in the control variable are obtained in the case of two space dimensions $(d=2)$. Numerical experiments are provided which support our theoretical results.

Thursday, 27 April
Madhava Lecture Hall


Neetu Garg A Numerical Study for a Class of Time-Fractional Burgers Equations This talk focuses on the numerical study for a class of time-fractional Burgers equations with the Dirichlet boundary conditions. These equations occur in fluid dynamics, turbulent flows, acoustic waves, and heat conduction. We employ the Crank-Nicolson finite difference quadrature formula to discretize in time. We then use exponential B-splines to discretize in space. We present stability and convergence analysis. Numerical experiments are presented to illustrate the efficacy of the proposed method and consistency with the theoretical analysis.
Eylem Ozturk* THE LIMIT CASE FOR THE p−LAPLACIAN EQUATION WITH DYNAMICAL BOUNDARY CONDITIONS In this talk we study the limit as $p\to \infty$ in the evolution problem
driven by the $p-$Laplacian with dynamical boundary conditions. We prove that the natural
energy functionals associated with this problem converge in the sense of Mosco convergence to
a limit functional and therefore we obtain convergence of the solutions to the evolution problems.
For the limit problem we show an interpretation in terms of optimal mass transportation and provide
examples of explicit solutions for some particular data.
Diksha Gupta* Existence of high energy positive solutions for a class of elliptic equations in the Hyperbolic Space In recent years, many efforts have been made to generalise scalar field-type equations for non-local operators in the Euclidean space or in domains after their connection with various physical problems. In the hyperbolic space, Sandeep-Mancini have shown
the existence and uniqueness of finite energy positive solutions of a homogeneous elliptic equation.
Inspired by this, we investigated whether positive solutions for a perturbed problem can still exist.
Precisely, we studied the existence of positive solutions for the following class of scalar field problem
-\Delta_{\mathbb{B}^N} u - \lambda u = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad
u \in H^{1}{(\mathbb{B}^{N})},
where $\mathbb{B}^N$ denotes the hyperbolic space, $1<p<2^*-1:=\frac{N+2}{N-2}$, if $N \geqslant 3; 1<p<+\infty$, if $N = 2,\;\lambda < \frac{(N-1)^2}{4}$, and $0< a\in L^\infty(\mathbb{B}^N).$ This variational problem lacks compactness in the subcritical case because of the {\it hyperbolic translation\rm}. Firstly, we performed a detailed analysis of the Palais-Smale decomposition associated with the corresponding energy functional. We then established a series of energy estimates involving {\it interacting hyperbolic bubbles.\rm} The evaluation of these estimates needed to be tackled very delicately since the hyperbolic volume grows exponentially with the radius, i.e., $\mathrm{~d} V_{\mathbb{B}^{N}} \asymp e^{(N-1) r},\;r \rightarrow \infty$ unlike the polynomial growth $r^{N-1}$ of volume in $\mathbb{R^{N}}$. Finally, we proved the existence of a positive solution by introducing the min-max procedure in the spirit of Bahri-Li in the hyperbolic space by suitably defining a \textit{center of mass} type function and using a \textit{topological degree} argument.
Aarti Patle On injective dimension of generalized Eulerian graded D-modules in char

p > 0

Let R be a polynomial ring in n indeterminates with coefficients in a field K of characteristic
p > 0 such that [K : Kp] < ∞, and D be the ring of differential operators over R. In this pa-
per, we prove that the minimal injective resolution of a generalized Eulerian graded D-module
M terminates in the direct sum of indecomposable with certain finiteness properties in case of
characteristic p > 0. Consequently, we provide the best possible lower bound for the injec-
tive dimension of a graded D-module T (R), where T is any graded Lyubeznik functor on the category of R-modules.
Shyamsunder* A brief Introduce of Fractional Calculus Who first gave the theory of how fractional calculus was born and how it developed? What Formulations and Applications of Fractional Calculus in Daily Life? A brief description of these concepts has been given.
Oorna Mitra The conjugacy problem and other related algorithmic questions in groups In this talk, we will introduce some algorithmic problems in groups, namely the twisted conjugacy problem (TCP) and orbit decidability (OD), which are closely related to the classical conjugacy problem (CP) in groups. We will state some new results towards solving the CP in certain extensions of the solvable Baumslag Solitar groups, using a strategy developed by Bogopolski-Martino-Ventura (Orbit decidability and the conjugacy problem for some extensions of groups. Trans. Amer. Math. Soc. 362 (2010), no. 4, 2003–2036), which gives a way of solving CP in certain extensions of a group by solving the TCP in the group. This is based on ongoing joint work with Mallika Roy and Enric Ventura.